Milan ended up holding on to win the game 2-1, courtesy of two goals from Giampaolo Pazzini, but an own goal from Philippe Mexes in the 84th minute gave Bologna hope of snatching a point.
Speaking to reporters after the match, Allegri said his side needed to convert their domination in matches into more goals.
"Today the team played well, above all in terms of technique after we raised the intensity level," he said.
"Clearly we’ve got to finish off games, instead we risked throwing it away at the end.
“We’ve got to improve, as we cannot dominate a match to this degree only to risk compromising it with moments of naivety. It would’ve been tough to swallow a draw this afternoon.”
Fiorentina, Napoli and Lazio all dropped points this weekend, meaning Milan's win sees them well in contention for a Champions League spot, but Allegri was keen to play down expectations.
“There are many teams in this race and we will try our best, but unfortunately when making so many changes to a squad you must expect this sort of situation.
“Many clubs have been left out of the Champions League in recent years, so it could be our turn, but we are targeting more long-term prospects.
“Our objective is to end the season on an upward swing.”