Spurs have finished fourth in two of the last three seasons and returned to the Champions League places last weekend after a 2-1 victory over Southampton.
Huddlestone, who missed nearly all of last season through injury, has started the past two Premier League games in the absence of Mousa Dembele and is now determined to help Spurs qualify for the Champions League again.
"I like to think the top four will be our natural habitat as a club," the 25-year-old told the Daily Mirror. "We've been to the Champions League before, we're aiming high again and it's good to be back.
"Basically I've lost nearly 18 months of my career to injury at a time when I should be coming into my prime.
"I had half-cemented a place in the team, we had finished fourth under Harry Redknapp and we were going well in the Champions League when I first picked up the ankle injury, and it was the start of a long struggle.
"Last year was a write-off and a nightmare, especially watching the lads do so well up until February, when they were in with a chance of the title, and then not being able to help out when results dipped a bit.
"Luckily, since we reported back for pre-season, I've been fully fit and I've enjoyed being involved with the boys again."