The Canaries’ last outing was a 6-1 thrashing at the hands of Manchester City and they are currently in 11th place and on par with the two teams above them on 43 points.
Midfielder Surman concedes that the squad are wary of falling down the league in the final games and insists the players must not ease off during their run-in.
The 25-year-old told The Norwich Evening News: "You want to finish with a positive frame of mind heading into the summer, and we want to finish as high as we can in the Premier League because the higher we finish the more of an achievement this is, so we want to keep pushing.
"We don't want to let the season peter out and we end up finishing 16th or 17th. We want to really push on and see if we can finish in the top half.
"We are not in a relaxed frame of mind yet and I don't think the gaffer allows that really. Everyone wants to finish with a flourish and see how many points we can get.”
He added: "We've got some big games coming up with Blackburn, Liverpool, Arsenal and Villa. They are all top sides in the Premier League so they're going to be tough, we know that.
"And we know if we take our foot off the gas you can end up being on the end of a hiding again, like Saturday.
"So we need to push through and end the season on a high. We've got four games left and we'll aim to get 12 points out of those four games, and there's no reason why we shouldn't."
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