The Italians dominated for the most part and while Stephan El Shaarawy headed them ahead on 15 minutes, Tim Matavz ensured the tie remained poised ahead of next Wednesday's return in Italy.
"We are disappointed because we are commenting on a draw that could have been a victory," Allegri said.
"We struggled at the beginning of the game, after the advantage we had a couple of chances to double the lead. We played a good game against a team that has played its sixth game of the season and is very skilful.
"In the first half we read some situations incorrectly while in the second half defensively we were good.
"We won the ball back well in the second half, but we were too far apart in the first.
"We are disappointed not to have won."
El Shaarawy admitted his side's failure to finish has left them with a tricky return leg at the San Siro next Wednesday.
"Hopefully we will go through but they are a very good side," he said.
"We know it will be a difficult game at the San Siro.
"We had a couple of chances to double the lead and they equalised when we were on top.
"We are pleased with the performance, we played the game at a good tempo as they were more match fit than us."