"Harry is brighter and also more tactically astute than people give him credit for - his record tells you that," Mabbutt told the Daily Express.
"It's a big opportunity for him to change a few people's perceptions, because the aspirations of Tottenham are much greater than Portsmouth, Southampton or West Ham and he will be under far more scrutiny.
"When that extra pressure is put on you, the rewards are far greater. Tottenham is the stage from which he can say, 'I'm one of the best managers'. Everyone knows he is a great character and that has come across in the Spurs' dressing room. But there is more to Harry than that.
"We were 4-2 down at Arsenal and the heads could have gone down - but we fought back and got a draw.
"Then we were losing against Liverpool but we won.
"The heads didn't go down once and that's because of Harry. There is now a never-say-die attitude. But he also made very important tactical decisions in those games that helped turn the result in our favour.
"Harry has been very positive. Sometimes, when it's all going against you, you put on another defender for damage limitation. But he has always been positive and risked a thrashing to get a result. Every decision has worked.
"Whatever he does now will be taken on board and will carry far more weight than anything he's done previously because he is on the big stage at Tottenham."