The Bianconeri were a long way from their fluent best against a stubborn Sporting outfit, who took an unlikely early lead through Alex Sandro's unfortunate own goal.
A superb Miralem Pjanic free-kick pulled the Italians level after 29 minutes before Mario Mandzukic headed home with just six minutes remaining to secure three points that move Allegri's side up to second in Group D.
Mandzukic's goal was Juve's only clear attempt in an insipid second half and Allegri was quick to point out a number of reasons for their sluggishness as they scraped a first win in three games.
He told Mediaset Premium: "We are not sharp right now, as some players were out for a while, others returned from international duty in bad shape, so we must continue to work.
"It's never easy to win in the Champions League, we've made a step forward, but there's a long way to go and we must try to reconnect, as some of our elements are a bit disconnected.
"We made some technical errors, especially in the opening 20 minutes, then at the end we were running a lot of risks rather than locking down the result.
"At this moment we need to rediscover our solidity, which I think we did have tonight when Sporting had the ball, but naturally our fitness levels and sharpness must improve and we can only do that via training."