The Bianconeri, finalists in two of the last three campaigns, head to Wembley Stadium on the back of a 2-2 draw in last month's first leg.
After ceding possession and allowing their opponents to dictate the flow of the game in Turin, Allegri has confessed that his side must produce a far better display on Wednesday night.
Despite acknowledging that the second leg is 'like a final' for the Italian champions, though, Allegri - ready to unleash fit-again duo Paulo Dybala and Gonzalo Higuain in North London - is adamant that Spurs will also feel the weight of expectation.
"Considering the first leg result, there's more pressure on them because they are the favourites," he told reporters at his pre-match press conference.
Asked about his team selection, Allegri added: "Both Higuain and Dybala will play. Higuain has been taking part in training for two days, so he is at our disposal and ready to play.
"Dybala is fully fit, as seen against Lazio, but tomorrow is such an important game that they all want to be a part of it, even if not at 100%.
"There is a good chance that Douglas Costa will play, too. They could all play together, they might not. I've only got those three, so some of them have to play! Maybe I'll remove a midfielder!"
Juve have won five of their previous eight last-16 ties in the Champions League, most recently easing to a 3-0 aggregate victory over Porto 12 months ago en route to reaching the final.