Frank Hadden believes the 26-6 victory over Italy - Scotland's first in three outings - could force his side into the Six Nations title race.
"I feel we are back in the championship now," the coach told BBC Scotland. "It is going to be a very tight championship after France beat Wales.
"We could do with a good result against Ireland and that could make for an interesting couple of weeks.
"People said you need one win - a roll starts with just one win."
Hadden played down any pressure following suggestions that defeat to Italy - in what many considered the wooden spoon decider - would have made it difficult for him to retain his job.
"For me personally, I certainly did not notice," he said.
Hadden happy with untidy win
"I have been a professional coach for 10 years now and there's pressure all the time.
"The minute you succumb to that pressure is the minute you lose your focus."
Hadden admitted that it was difficult to gauge his side's progress from the defeats by Wales and France considering Italy's particular style of play.
"It's hard to say as it can be very untidy against a rush defence," he said.
"You don't get the same kind of rhythm that you do against a sliding defence, as we had in Paris.
"What you tend to get is a lot of slower ball, but you can cut right through and we had two or three opportunities that we did not capitalise on and I think that would have made it a really interesting scoreline."
Hadden was looking forward to the visit by Ireland, who later went clear at the top of the Six Nations by beating England to record their third straight win.
"We're delighted to be playing them at home as they are playing exceptionally well," he said.
"But they are an entirely different kettle of fish than playing against Italy, who are always awkward to play against.
It just feels good to be out there playing, getting opportunities
Scotland try-scorer Simon Danielli
"They hold on to the ball for long periods and their defence always puts you under pressure, but on a couple of occasions we looked like we knew how to unlock their defence."
Scotland wing Simon Danielli scored a fine try in a man-of-the-match display.
"I thought we really deserved it," he said after his first international score for five years.
"Obviously, when you've had a run of injuries and there's really good the strength in depth, you've just got to bide your time. I was fortunate to get the opportunity and really pleased.
"The forwards were really good today, they gave the backs some space.
"I've had quite an injury-prone season, so I'm fairly fresh. I've just played six or seven games. It just feels good to be out there playing, getting opportunities."
Italy head coach Nick Mallett claimed his side were on the wrong end of some 50-50 decisions by Nigel Owens but refused to blame the referee for his side's third straight defeat in this year's tournament.
"I'm certainly not complaining about the referee and I'm not saying that was the reason we lost the game," he said. "That was not the case whatsoever.
"But I think on two or three occasions I saw at half-time, for example, there were two or three penalties that were given against us that I felt were a bit harsh."
Mallett once again faced questions about his team selection following his decision to play Andrea Marcato - nominally a fly-half - at full-back and Luke McLean - nominally a full-back - at fly-half.
"If you like to play rugby the way we would like to play, you need a number 10 who has got some physical presence and who can take it to the line and not lose the ball," he explained.
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