Weeden finished 17 of 26 for 158 yards with one touchdown and an interception on a pass that was tipped at the line and returned 53 yards for a touchdown by Steelers linebacker Lawrence Timmons just 1:11 into the game.
Shurmur gave a somewhat mixed review on Weeden's outing.
"He did some good things in that football game," Shurmur said. "But as we move forward and get ready to play the Raiders, there's some things that he can clean up that'll help us have a better performance next week."
McCoy went 4-9 in 13 starts last season before he was injured. The three-year veteran, who was thrust into a starting role for eight games as a rookie because of injuries, had assumed he would start this season. However, he lost his job when the Browns drafted Weeden in the first round of April's draft.
Shurmur is confident McCoy can step in and perform well if he's called upon to play.
"If Colt goes in the game, I expect he's going to function fine and help us win games," Shurmur said. "I have all the confidence in the world in Colt. Colt has handled his situation this year in a very professional way. I don't see any reason why he can't go in and function well."
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