Moise Kean earned the credit for Juve's winning goal in Sunday's 1-0 win at home to Roma as Rodrigo Bentancur's first-half header deflected off his forehead and in, while Wojciech Szczesny saved Jordan Veretout's penalty.
Juve have now won four consecutive Serie A matches and six in a row across all competitions, though they started the 2021-2022 campaign without a win in three league fixtures – losing back-to-back matches after drawing its opener.
"We have players more suited to counter-attacks, those are their characteristics, so when we try to play the ball, we either fall asleep or get irritable," Allegri – back in Turin for a second spell having replaced Andrea Pirlo – said.
"It's an important victory, another step forward in the table and a further progress for the season. We were missing [Paulo] Dybala, [Matthijs] De Ligt, [Adrien] Rabiot, [Alvaro] Morata only came on at the end, but when everyone plays with that spirit, you don’t concede as many goals.
"We are starting to slow the game down at the right time, but we need to step up the pace too when it's required. I won't lie, I probably did damage too at the start with some of my choices, I had to get to know some players and their characteristics, but we're getting there."
"We knew beforehand it would be tough. Roma could've deserved a draw, but these are games that depend on incidents and tonight fortunately they went our way," said Allegri. "I do say they put in a good performance and are one of the best teams in the league."
After falling behind in the 16th minute, Roma's Tammy Abraham thought he had equalised, turning a loose ball into the back of the net after Szczesny brought Henrikh Mkhitaryan down in the box.
But the whistle had already gone to award Roma a spot-kick, which Veretout saw the Juventus goalkeeper parry aside on the stroke of half-time.
"I like 1-0, as it's a good result, especially as we kept another clean sheet," Allegri added. "Roma are a technically good team, they have a lot of quality and caused us problems early on, then we scored a good goal and improved as time wore on."
Szczesny is the goalkeeper who has saved the most penalties in Serie A in 2021 – three out of the seven faced.
On the penalty, Allegri said: "Szczesny made all his mistakes for the season in one fell swoop and is now bringing back what he can to the team. We need to improve in the final third, the timing and movement, but we'll get there."
With this win against Roma, Juventus has won 10 Serie A games at Allianz Stadium against a single opponent for its first time.