The Potters find themselves 14th in the league table with 13 points from 12 matches, just three points above the relegation zone.
If Stoke lose at Everton on Saturday, then they could fall further down the standings, but Begovic insists that he is not worried and has also praised manager Mark Hughes.
"There's no panic here, our confidence isn't lacking," he told the Stoke Sentinel.
"We have performed really well but have not got the results which we have desired, but we are trying our best to rectify that.
"The gaffer has given me a lot of belief. We have a great goalkeeping coach in Andy Quy who helps me a lot and helps me get better.
"It's a good working environment for me and I try to get better each and every day."