The Republic of Ireland international could not prevent City slumping 2-0 at Fratton Park over the weekend and the loss drew stinging criticism from boss Mark Hughes.
Given, who left Newcastle to move to Eastlands in the winter transfer window, is now determined that he and his team-mates will banish the memory of their lacklustre performance on the South Coast when they travel to FC Copenhagen on Thursday.
"Last weekend at Portsmouth was a huge disappointment for everyone involved with the club," Given - who looks set to make his European debut for his new club - told the Manchester Evening News. "On the day we were not good enough and we need to rectify that.
Favourites"Whenever you have a bad performance it is great if the next match comes quickly and you can immediately start to put the record straight.
"Hopefully we can do that on Thursday day. We know that we let the fans down at Portsmouth when we were not good enough on the day."
The 32-year-old is also excited by the prospect of playing in the Uefa Cup, after sampling European football with Newcastle, and has suggested City could win the competition.
Bookmakers have City as second favourites to sample glory at Istanbul's Sukru Saracoglu Stadium on 20th May, behind Italian giants AC Milan, while domestic rivals Tottenham and Aston Villa are also contenders.
DesperateAnd Given admits City - who have not lifted a major piece of silverware since the 1976 League Cup - are desperate to win the competition.
"There are some huge teams both in terms of ability and history still left in this year's Uefa Cup and though some people view it as a poor relation to the UEFA Champions League it still takes some winning and particularly so this season," he added.
"It is a huge trophy in terms of kudos for any team to win and I am sure all the teams left in it are as desperate to win as we are.
"It is just nice to be back in Europe again and it is great to be in with a chance of winning a trophy. Who knows which team's name is on the cup? It could be ours."