Lallana, now part of the coaching staff with Southampton, played for De Zerbi at Brighton.
He told talkSPORT: "Definitely (De Zerbi will keep Spurs up). Not even a doubt in my mind. I just think they're very, very fortunate. I'm actually slightly jealous.
"I was speaking to a player at Spurs who was picking my brains about him. I just know they're going to be in for a rollercoaster, but a great one."
Lallana continued: "I always compared him with Jurgen, actually. Probably just the passion that they both possess for the game. I think tactically and game mode-wise, they're completely different. But in terms of love and passion for football, they're exactly the same.
"He'll know he's not got time to play a certain way, a certain style. He won't be snobbish to not understand that. He knows he's got to go in there and motivate a group of men.
"Luckily for Roberto, he might not know that, but he's one of the most inspirational managers and people there is, in my opinion. After five minutes of him speaking in our first meeting when he joined Brighton, I was on board."