Walters headed in two own goals and missed a penalty as the Potters were beaten 4-0.
"I don't think anybody will worry about Jon Walters," Begovic said.
"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 I am sure he will probably score a goal on Tuesday."