Fifa has refused to comment on mistakes made by officials in Sunday's World Cup last-16 ties, or the potential future use of goal-line technology.
England's Frank Lampard was denied a goal against Germany, despite his effort having clearly crossed the line.
And Carlos Tevez's first goal for Argentina against Mexico was allowed to stand despite him being offside.
At its daily briefing on Monday, Fifa spokesman Nicolas Maingot said it was "not the place" to discuss such issues.
"We will not enter into any debate on refereeing at the daily media briefing. I am not competent to do so," explained Maingot.
Fifa offers no comment on ref blunders
"The International FA Board (IFAB), which Fifa is a member of along with the four British associations, dealt with this topic in March. A clear decision on the use of technology was taken at the time.
"I don't think football is very much different from other sports and not all sports have recourse to technology."
Maingot added that Fifa will be cracking down on World Cup match action being shown on stadium giant screens after replays of Tevez's disputed goal against Mexico sparked arguments on the pitch.
Maingot said the replaying of such incidents "should not happen" and will be more tightly controlled at future matches.
Fifa president Sepp Blatter, who has voiced strong opposition to the introduction of goal-line technology, was in the crowd at Free State Stadium in Bloemfontein for England's 4-1 second-round defeat by Germany as Larrionda and his assistant Mauricio Espinosa failed to spot that Lampard's 38th-minute shot had dropped well over the line.
After the game, Chelsea midfielder Lampard advocated the use of video technology to help referees.
"We had a meeting before the World Cup when we were told about a million different rule changes that hardly affect the game," he said
"The big one, the one that affects the game, hasn't been brought in so it is a no-brainer."
International players' union FIFPro added their voice to calls for technology and criticised those who opposed its introduction..
"We can do it, the football world wants it and yet it is still being thwarted, that is unacceptable," said Tijs Tummers, secretary of FIFPro's technical committee.
"There is not a single convincing argument against the use of goal-line technology. With offside incidents, it is slightly more complicated, but the Argentinian goal which was allowed to stand shows the failure of the system even better.
"Referee Roberto Rosetti had a long consultation with the assistant referee, who was in contact with the fourth official via a microphone.
"He would undoubtedly have heard that Tevez was offside, the whole stadium had already seen it by then via images on the scoreboard.
"Yet, because the referee was not allowed to rely on video images, he had to award the goal which he knew should have been disallowed.
"You could see the doubt in his eyes. Technology does not undermine the authority of referees, it only helps them."
Blatter has claimed that stopping matches to consult video technology would break up the rhythm of the game and possibly deny a team the opportunity to score a goal.
However, the inventor of Hawk-Eye has said Uruguayan referee Larrionda would have known within half a second that Lampard's shot had crossed the line.
Goal-line incidents are the only decisions which are entirely definitive and the answer can be provided to the referee within 0.5 seconds of the incident happening
Dr Paul Hawkins
Inventor of Hawk-Eye
Dr Paul Hawkins, whose technology has been successfully introduced into tennis and cricket, is confident he has the system to end the debate over goal-line controversies once and for all.
"Goal-line incidents are the only decisions which are entirely definitive and the answer can be provided to the referee within 0.5 seconds of the incident happening," said Dr Hawkins.
"This makes a clear distinction between goal-line and other decisions. Referees want goaL-line technology. It would be there to help them, not to replace them."
England were 2-1 down when Lampard's effort was ruled out.
It was a pivotal moment for England, who went on to lose 4-1, as they had just pulled a goal back through Matthew Upson after falling behind to strikes from Miroslav Klose and Lukas Podolski.
"It was a clear goal - 40,000 knew it and I knew it, but there were two people that didn't," added Lampard. "It certainly affected the game and we're bitterly disappointed."
Germany keeper Manuel Neuer admitted his side were lucky not to have conceded.
"I tried not to react to the referee and just concentrate on what was happening," said Neuer. "It was difficult. I knew it was close.
"Then I saw it on the television in the doping control office and what actually happened. I knew it was tight - probably about two metres!"
Tevez puts Argentina into controversial lead
The failure to spot the ball had crossed the line came hours before Mexico were the victims of a controversial decision during their 3-1 defeat at the hands of Argentina in their last-16 clash.
With the game goalless, Tevez headed Argentina ahead despite being yards offside when played through by Lionel Messi, a mistake that was confirmed when the incident was replayed on the stadium's big screen shortly after a goal had been awarded.
Maingot added that Fifa has yet to received feedback about a mass confrontation between coaches, players and officials behind the Mexico bench as the teams left the field at half-time.
Mexico coach Javier Aguirre claimed the officials' blunder had ruined years of preparation in a matter of seconds.
"We were stronger up until the first goal and then after the mistake the match changed dramatically," Aguirre stated.
"After the referee gave that offside goal we lost our concentration. Referees and linesmen can take split-second decisions and they can spoil everything and years of hard work."
Fifa has consistently refused to entertain the idea of using goal-line technology and video replays, a position underlined less than four months ago by the IFAB.
But former England skipper and BBC pundit Alan Shearer said: "All the managers and the stars of football are calling for it. Not everyone can be wrong, can they?"
Tottenham boss Harry Redknapp thought Fifa president Blatter should be "embarrassed".
Redknapp continued: "We've all seen it on the replay - it was just amazing. That was a clear-cut goal and it was absolutely vital to England and it wasn't given. Technology has got to come into games."
Redknapp's sentiments were echoed by England manager Fabio Capello.
"It was the most important moment of the game," he said. "Where is the technology? Instead we are talking about goal or no goal."
UK Prime Minister David Cameron, who watched the game with German Chancellor Angela Merkel at the G20 summit in Canada, added his weight behind the calls to introduce video technology to football.
"I'm a keen follower of cricket and tennis and I think the third umpire has been a great thing and the machines that bleep at Wimbledon are quite handy, too," said Cameron.
"Maybe that's something that football could now have a look at."