The Republic of Ireland striker scored two own goals and then missed a second-half penalty as the Potters succumbed to a 4-0 defeat at the hands of the European champions.
But the Bosnian goalkeeper believes that Walters will atone for his errors in the FA Cup third round replay tomorrow night with Crystal Palace.
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“I don’t think anybody will worry about Jon,” Begovic told reporters. “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’s a big enough character to bounce back and I am sure he will probably score a goal in the cup.”
The defeat to Chelsea was the Potters’ first of the season at home and despite a valiant first-half effort, they capitulated in the second and missed the opportunity of a consolation goal with Walters’ penalty miss.
"I’m very disappointed," Begovic added. "We knew it was going to be a tough game. They’re the champions of Europe and they overpowered and outplayed us in the second half.
"One freak incident happened for the first goal and fortune was on their side. That set us back just before half-time. It was unfortunate and I don’t think we deserved to lose 4-0.
"We gave a pretty decent account of ourselves for most of the game. But with their class and ruthlessness they punished us.
"We sorted a couple of things out we could have done better, and we were well in the game in the first half. But some things hadn’t gone our way."