The 36-year-old was dropped by new Villa boss Paul Lambert after the 3-1 defeat by Everton in August and has made only one appearance, in the Capital One Cup, since, with Brad Guzan preferred in the Premier League.
Given told talkSPORT: "Frustration can sometimes boil over when you're not playing, but for me it's important that I keep my head down and work hard and please God my chance comes round again."
He added: "I am gutted that I am not playing in the team, that's natural, and hopefully if I work hard I'll get back in the side."
Given is not the only Villa player to have to make do with a place on the bench recently, with striker Darren Bent only a substitute in the last two league games.
Given said: "He's frustrated a little bit at the minute of course but we've got (Christian) Benteke, who's a very powerful young forward, and he's done very, very well. It's competition for places and that's what we need."