The Italians edged Borussia 2-1 in Turin in the first leg on Tuesday and Allegri was pleased with the overall performance. Juventus travel to Dormund for the return leg on March 18.
“It was an important test for us after a difficult group stage,” Allegri said. “A last-16 tie is never easy, the right mindset is required.
“We came away with a positive result because the team played well.
“We knew how to be defend in an orderly fashion, in spite of the odd misplaced pass.”
He added on the official club website: “We are happy with the win and the display put in by the players.
“The only regret is that we could have won by a greater margin.”
Juventus led 2-1 at half-time thanks to goals from Carlos Tevez and Alvaro Morata, but wasted five opportunities to increase their advantage after the re-start.
“We had several chances and performed well in the second half,” Allegri said. “Borussia are a team who operate with pace and we didn’t give them an inch.
“It was a very tactical encounter.
“We played the type of game we needed to in a Champions League last-16 tie, where all the meetings are evenly poised.
“I expect the return leg to be extremely difficult because we will play in Dortmund and Borussia play a different way when playing at home.
“But we will be ready for the game.
“Now we’ll think about recovering our strength for the game with Roma and in due course we will turn our attentions to the second leg in Dortmund.”
Serie A leaders Juventus can extend their nine-point advantage over nearest rivals Roma on Monday when the two sides square off at Rome’s Stadio Olimpico.