Barca completed the greatest comeback in the competition's history against Paris Saint-Germain at Camp Nou on Wednesday, overturning a four-goal first-leg deficit to win 6-1 on the night and 6-5 on aggregate.
Three of their goals came from the 88th minute onwards and Allegri conceded it was an occasion for the history books.
But he felt Barca's progression to the last eight means there are now three teams who should be considered favourites over his Juve side.
"With all due respect to Paris Saint-Germain, to have Barcelona in the quarter finals – and I know we still have to get there ourselves – is not pleasing," he told reporters ahead of Friday's home Serie A match with AC Milan.
"Something like what happened to Barcelona in Paris, where they lost 4-0, doesn't happen every year, or even every five years.
"It was a beautiful evening of football which I think will remain in the annals of football history, because I don't think any team has ever pulled off such a good comeback.
“It wasn't easy for them, it was a good and very intense game. It wasn't great technically, compared to what Barcelona have always shown the world, but that is why football is beautiful and strange - there are situations no-one can predict."
Allegri wants Barcelona's thrilling turnaround to serve as a warning for Juve when they play their own second leg against Porto in Turin on Tuesday with a 2-0 lead in hand.
He continued: "Above all, that should make us understand and reflect that on Tuesday we have a game in which we have a two-goal lead and in the league we have an eight-point lead but it is not over.
"So we have to take things one game at a time, without looking at what might happen in three months."