The Canaries slipped out of the top-flight for the first time in three years - finishing just three points short of safety in 18th place - and they will now look to repeat their promotion-winning feats of the 2010/11 campaign.
Manager Neil Adams has already boosted his squad with the signings of Lewis Grabban from Bournemouth and Kyle Lafferty from Palermo, although winger Robert Snodgrass has departed to join Hull City for a reported £7million.
Last summer’s big-money arrivals including the likes of Ricky van Wolfswinkel, Leroy Fer, Gary Hooper and Nathan Redmond all currently remain at the club, and Surman believes that the quality is there to push for promotion.
"We have more than enough in this dressing room to be in the Premier League. That is the main aim and that is the attitude we are taking into games," he told the Pink ‘un.
"We have some decent players and good characters in the dressing room. When you first come back in everyone is on a downer after the relegation but the manager has had a few meetings and made it clear that is in the past and that has gone now.
"Things can change so quickly in football. It was disappointing last season with what happened and the manager leaving but everyone is behind Neil. He has put his stamp on things and we all know what he wants."
Surman found himself out of the picture under former boss Chris Hughton last season and was subsequently loaned to Championship side Bournemouth, but he is now hoping to become a more prominent figure with one year remaining on his current deal.
"I had a bad injury, missed the whole season through it really and going to Bournemouth just allowed me to find that touch, that missing yard back and probably gave me back my belief as well to feel I’ve got my career on track," he said.
"It’s nice to feel wanted but I am not sure exactly what is going to happen at this moment in time. I’m trying to get the most I can out of the games and we will see what happens in the future. I really enjoyed it at Bournemouth but it is nice to be back and everyone is playing for a place here."