Stoke's Ireland international had a nightmare against Chelsea as he scored two own goals and then blazed a penalty against the top of the bar in a 4-0 battering.
Begovic said: "I don't think anybody will worry about Jon Walters.
"His character and personality won't be affected by anything that happens to him. It was a couple of unfortunate incidents for him.
"I take the blame for the second goal because I probably should have come for the ball - but seeing him there I decided not to.
"He is a big enough character to bounce back - and he will probably score on Tuesday."