But Livi boss Jim Leishman had little sympathy, saying it was just "tough" for his Uefa Cup opponents.
The Croatian official claimed that he had already blown for full-time before a shot from midfielder Marius Zarn struck the net with the scores level after two legs.
All three minutes of time added on had already been played, but Vaduz believe that he should have not blown his whistle until action from their corner kick had ended.
"It was the same moment that I shot the ball. I have never seen this before.
"I hope the referee will be a little bit embarrassed because he knows he made a mistake."
Vaduz coach Walter Hormann will speak to his club's president about lodging an appeal with Uefa but admits that his side have no chance of changing the outcome.
The Vaduz backroom staff chased after the referee at the end of the game and the official had to be escorted from the field.
"I am a little bit angry at this moment," said Hormann.
"I am a very emotional coach and I ran to the referee after the game and I said bad, angry words to him.
"But he would not speak to me. He said nothing at all."
Hormann believes that perhaps the referee favoured Livingston because they are a bigger club.
But he insisted he had no grudge against the Scots and wished them well in the next round.
Livi manager Jim Leishman admitted that he thought his side's European dream was over when Vaduz struck.
Instead, with his side having drawn 1-1 in Liechtenstein, the 0-0 draw in West Lothian was enough to take them through on the away goals rule.
"It all happened so quickly. But, to be honest, I thought at first it was a goal and I said to myself 'we're out'," he said.
"Then John Robertson explained to me what happened and I don't really care now. I'm just glad that we're through.
"The fourth official said that there were to be three minutes added on and, after more than two minutes, Vaduz won a corner.
"Apparently when Zarate cleared the ball, that's when the referee blew the whistle and then their guy had the shot."