Harry Redknapp's side are currently fifth place in the Premier League but sit four points behind Manchester City with only five games remaining and after an impressive run in the Champions League this season, the White Hart Lane club will be hoping for the same chance next season.
Huddlestone told Sky Sports: "It was a disappointing result against West Brom but we can't dwell on that for too long. We have five cup finals now."
His remarks come after Spurs drew at home with West Brom last week and Huddlestone wants the side to bounce back when they meet Chelsea on Saturday and refind the spark they have been missing.
"Nothing too hasty was said in the changing room after. We are all pulling in the same direction.
"I think we were just missing a little bit of spark and on another day maybe a couple of players would pull something magic out of the bag and we would have won the game but it wasn't to be."
Spurs reached the quarter-finals of the Champions League this season and the experiences have made Huddlestone hungry for more.
"We don't want to be hanging on for fifth position. We have to look up and we want to finish where we were last season," he added.
"Once you have had a taste of the Champions League, you want more. Maybe we're getting a bit greedy but we have shown that we can compete with the best in the competition, so to not be in it next year would be very disappointing.
"We have still got games to play though so as long as it's possible then we won't give up."