The Spurs youngster was substituted as his side saw out a 1-1 draw with Liverpool at Anfield on Saturday.
"He has great skill, great energy, and a wonderful awareness on the pitch."
Anderton went on to praise Alli's composure, whilst also highlighting his combative style of play:
"When he gets in the box, he's cool as a cucumber, great finishes, great strikes, but he also gets stuck in and makes tackles, he's a team player."
In response to comparisons with Paul Gascoigne, the former Portsmouth and England winger responded by saying while it is great for Alli's confidence, his manager will not let him get ahead of himself:
"In Pochettino, he's got a great manager to help and nurture him through."
Alli has been in scintillating form for his club this term, racking up seven goals and 11 assists in 42 games. He has been a key component in the Spurs team as they continue to chase down Leicester City at the summit of the Premier League.
He has also proved his worth on the international stage, making six appearances for England, all before his 20th birthday.
Spurs have two tough fixtures on the horizon - a home fixture against Manchester United before a tricky away trip to Stoke City. With Leicester winning at home to Southampton, the North-Londoners will surely need to take six points from those games to keep in touch at the top.