The Bianconeri left it late at the Stadio Olimpico on Saturday, Paulo Dybala marking his first start since overcoming a hamstring problem with a dramatic winner in stoppage time.
However, Juventus must now forget about domestic duties and focus on their Champions League clash with Tottenham at Wembley, with the last-16 tie delicately poised following a 2-2 draw on Italian soil.
"It wasn't an easy game for us," Allegri told Mediaset Premium after the 1-0 win in Rome.
"They are very strong physically, so it certainly wasn't going to be easy to play at the Olimpico. We had some injuries up front but the players did well.
"We wanted to come away from Rome with a positive result and that's what we got. They defended themselves very well and we knew that it was going to take something special to beat them.
"Yes, that special moment came from Paulo. He is a great young player and we are all happy that he scored.
"Tottenham are different compared to Lazio, they don't defend as well. This win certainly helps our confidence as we will have to be good and lucky on Wednesday."
Veteran defender Andrea Barzagli hopes Dybala's "amazing" goal is the first of many for the Argentine forward over the closing months of the campaign.
"He's just come back from injury and he's scored a huge, huge goal that has won us three massive points tonight," Barzagli told Juventus' official website.
"I think it will spur him on for the rest of the season now.
"Paulo is one of those rare players capable of trying something really difficult in the 92nd minute and pulling it off. His goal was just amazing.”