Dusan Vlahovic gave Juve a first minute lead before Tammy Abraham struck in the second-half.
“It is a long season, we even risked losing it on another corner towards the end," Allegri told DAZN.
“Juve played well on a technical level, but we must still improve. Roma were more defensive on their right in the second half and we should've put more crosses in with Weston McKennie on our left.
“I am happy with what the lads did, it was a good game, Roma are a great team and Jose is always good at keeping his side focused.
“It is unfortunate that Roma scored on the only corner they put to the back post, but that's football. It was a strong performance."
