The Old Lady will head into the second-leg of their quarter-final tie at the Bernabeu trailing 3-0 from last week's reverse match and they face a monumental task if they are to book their place in the last four.
Allegri knows his side will be up against it in the Spanish capital, but he insists they cannot afford to go chasing the game, and will instead adopt a patient approach.
"We cannot think of playing a game where we aim to overturn the scoreline in 20 minutes," he told a pre-match news conference. "We have to take it slow and then see what happens."
Despite urging caution, Allegri still believes Juve are capable of turning the tie around and he insists they can consider themselves unfortunate to be trailing by such a hefty margin in the first place.
The 50-year-old tactician added: "It was a harsh result for us but one we must accept. We have to play a great game and give our all for a positive result - and then you never know. Let's see what happens."