The City and Ireland international keeper also believes that should City qualify for a Champions League spot then that will help them attract more 'big name' players to Eastlands in the summer transfer window.
"It's pretty clear, we know we've got to try to finish fourth. If we don't, it would be a disappointing season," Given told BBC Radio Five live.
"There's pressure on the manager and on the players to try to deliver that.
"We'll push hard in the remaining games and hopefully get across the line and that would be good, to get Champions League football at Eastlands.
"That would be fantastic and I think it would help to attract a couple of players in the summer as well, to strengthen the squad and move the club forward."