The hosts took the lead through a first-half Matthijs de Ligt header, but Andrea Belotti equalised just after the hour mark and Juve struggled to create any meaningful chances in response, failing to hit the target at all in the second half.
The Old Lady remains in fourth place in Serie A, eight points behind leader AC Milan having played a game more, and just three points ahead of Atalanta in fifth, which has two games in hand.
Allegri, though, appeared to be satisfied with both the result and performance.
"It matters because, with the point, we followed up on the positive results we've had in the last two to three months," he said. "It wasn't easy, we weren't brilliant compared to Torino, but we played a good game.
"Paradoxically, we conceded a goal in our best moment. In the first half we had two or three situations where we could have scored, but not in the second half.
"Then we weren't very clean in the second half, but I think it's a normal path, it's natural when you're playing in the league, especially when you're aiming to be in the top four, so a draw isn't to be dismissed.
"I'd say the boys played a good game in terms of commitment and intensity. They tried to win until the end, so it's a point that we take home and allows us to extend the positive streak."
Allegri also seemed unconcerned by the performance of Dusan Vlahovic, who struggled to make an impact, having just one shot all game before coming off in the 74th minute.
The Serbia striker made a January move from Fiorentina in a transfer that could be worth up to €80 million ($126.5 million).
"He struggled because he's a very good player, but he has to learn a lot," Allegri added. "As many players have to learn. Tonight, he had to drag Bremer around the pitch and not give him any points of reference, because he is very strong on direct balls and less strong when you drag him around the pitch.
"Let's not forget that he comes from a team who are having a very good season, but he played one game a week. He's played six [here], so I think it's normal for him to grow. It amuses me because someone comes in and has to play every game.
"You have to grow, you have to get used to it, all the things you need in a great team, otherwise physically you can't manage to play a game every three days."
Daniele Rugani was withdrawn from the starting line-up ahead of the game after picking up an injury in the warm-up, while Luca Pellegrini and Paolo Dybala both came off with knocks, but Allegri did not seem concerned despite the upcoming UEFA Champions League Round of 16 first leg away at Villarreal on Wednesday (AEDT).
"I'm not worried at all also because during the season there are injuries and those we have and who are fit and enlisted, will play on Tuesday [Wednesday AEDT] against Villarreal and then we will prepare for Empoli," he said.