Spurs are still in the hunt for a Europa League place this season and Woodgate wants to continue their recent good form after the summer, echoing the sentiments of boss Harry Redknapp.
Redknapp wants to emulate the likes of Everton, who they face this weekend, by at least challenging for a top-four place in the Premier League even if they do not break through.
"I want to finish as far as we can up the league," Woodgate said. "The aim is always to get in the top four and the Champions League.
"We'll see how we do. It's going to be a better team next year, you can see how the team has changed under the manager we have now.
"Robbie (Keane) and Jermain (Defoe) have been good acquisitions for the squad, along with Wilson Palacios, who has been brilliant for us. It's taking shape in the training ground and we are starting to do it on a Saturday."