Walters headed in two own goals and missed a penalty as the Potters were beaten 4-0 by the Blues but Begovic has no doubt the forward is strong enough to bounce back, even backing him to find the net at the right end against Palace.
"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."
He added: "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."
The Chelsea defeat was 10th-placed Stoke's first at home in the league since February and the heaviest they have ever suffered on their own turf in a Premier League fixture.
It also means they have conceded seven goals in their last two games at the Britannia Stadium, having drawn 3-3 with Southampton on December 29.
Prior to that result, they had let in only four in their nine home top-flight matches for the season, and Begovic - who is likely to be rested for the cup tie - is optimistic the Potters can get things back on track in front of their own supporters in the contest with npower Championship outfit Palace.
"You always want to put things right and hopefully we can do that on Tuesday," Begovic said. "Crystal Palace will come here with nothing to lose.
"We appreciate the support from the crowd. We feed off it and it is important to have it. No matter what the result, they are always there cheering us on and we appreciate that. Hopefully we can put things right for them as well on Tuesday."