Allegri stormed off the bench and threw his jacket on the ground, seemingly in frustration, after the final whistle with his side having won only two of their last 14 Serie A matches.
"There are regrets, naturally we could’ve done better during this period, but football is vicious like that, sometimes it just doesn’t go your way," he told DAZN after the match.
"We risked losing a game that we were in a position to win at the start of the second half."
Despite four consecutive Serie A draws, Juve can still wrap up qualification for next season's Champions League in their next match against Salernitana.
They have also reached the Italian Cup final and will face Atalanta on May 15th.
"The important thing now is to concentrate on the next game, as that is the match ball for the Champions League, then we have the Coppa Italia final," Allegri said.
"The club will evaluate at the end of the season, naturally there are some solid foundations for Juve, but we were missing players like (Paul) Pogba, (Nicolo) Fagioli and, of course, (Federico) Chiesa was on and off."
Allegri also avoided discussing his own future at the club.
"I don't know, you’d have to ask the club. The important thing is for us to focus on the Coppa Italia final and hopefully, we’ll come back here with the Champions League already achieved," he said.
