Ronaldo scored twice as his club beat Sassuolo at the Allianz Stadium in a game which saw Juve's Douglas Costa sent off for spitting.
The summer signing from Real Madrid got off the mark for his new team in the 50th minute with a close-range finish and slotted in his second 15 minutes later.
The 33-year-old Portugal forward had two great chances to add to the brace, but shot off-target on each occasion.
Sassuolo pulled a goal back in stoppage time through Khouma Babacar before Costa sent off for spitting in the face of Federico Di Francesco after the intervention of the video assistant referee.
Allegri told the club's official website: "He came very close in his first three games.
"I think he rushed a couple of chances today – it looked like he was absolutely desperate to score.
"Football has a way of evening things out and that was the story of the first goal, with the ball bouncing off the post and sitting up for him. The second goal was brilliant. I'm happy for him.
Ronaldo was delighted to get off the mark for his new club.
"Sassuolo played well, but we showed good intensity and created a lot of chances," he added.
"I wanted to score, but the most important thing is to perform well and win matches.
"Of course there was a lot of attention on my move to Turin, but that's life. I'm happy, I'm working hard and my team-mates are really helping me to adapt to this league."
On Costa's offence, Allegri added: "These things shouldn't happen.
"The only thing we have to avoid doing this year is rising to the provocation. We had the game where we wanted it, but we started playing as individuals and not as a team."