"Freddie is a professional who made a mistake. It is rubbish to say he has not got a long-term future here," Jol said.
"His response since the Liverpool game has been excellent and this goal will have given him a lot of confidence.
"He is the complete player. He can head, pass and score a goal. We miss him when he is not playing."
Tottenham's win also came without the suspended Jermain Defoe and was their third straight clean sheet.
Spurs adopted a more attacking approach immediately after the departure of Jacques Santini but Jol admitted it was important to get back to basics after the 5-4 home defeat against Arsenal.
"It is not all about playing terrific football. We did that against Arsenal and lost," Jol said.
"It is about getting results and now that we are, we can work on our game at the training ground."
Spurs might have won more convincingly had Robbie Keane been sharper in front of goal but it was still the perfect result for chairman Daniel Levy, who is keen to rebuff any offers to buy the club.
He denied weekend reports that a consortium were poised to make a bid and install Glenn Hoddle as manager.
Levy said angrily: "We have never put up a 'For Sale' sign at this club and we are not about to do so."
