The Irish international has also admitted that the medal he earned when Manchester City won the FA Cup last year means little to him.
The 35-year-old failed to feature once in City's run to Wembley, as he spent the majority of his time at Eastlands as back-up to Joe Hart.
"I was happy for the team and the fans, but I didn't feel I had contributed because I didn't do anything," he said.
"Maybe I didn't deserve a medal. It's in the house somewhere.
"If I could win something with Villa, it would mean more to me. That has to be our target this season."
Given makes his home debut today against Blackburn Rovers.