Given was linked with a move away from Eastlands during the summer transfer window, but he remains a City player and is now determined to prove to Roberto Mancini that he is the man for the job.
Given said: "For me now the window has closed, that's gone. I have got to put my head down and work hard and try to get back in the team.
"I don't feel I have done a lot wrong since I have been at the club, so I suppose it's about proving the manager wrong and trying to work hard to get back in the team and if I get a chance, taking that and seeing how it goes.
"It is frustrating, but this is life at a big club which can buy as many players as it wants. You have got to be patient.
"But I am delighted to have played tonight and to keep a clean sheet was a bonus as well."
The Republic returned from Yerevan on Saturday with a priceless and hard-fought 1-0 win to leave their Group B rivals knowing they might have to do the same if they are to make the finals.
Asked if he expected the likes of Russia and Slovakia to be equally stretched, Given said: "I would hope so.
"I don't think there will be any teams who will come here and leave with an easy game, that's for sure.
"They have got some very good players and they caused us a lot of problems. But as a team, we stuck together and fought really well.
"We are really pleased with the way we have started. Hopefully we can get three points against Andorra on Tuesday night and that will set us up for next month, which is a tough month."
Russia at home and Slovakia away await the Republic in October, and that made Friday night's win imperative.
Given said: "We said before the game that if we have got ambitions to win the group, we had to come here and get three points, and that's not an easy thing to do.
"People say, 'Armenia, you should beat them no problem', but I think teams will come here and find it difficult.
"A clean sheet and three points, we are happy with that."