Sunderland were able to take a point from a hard-fought contest, with their goalkeeper Robin Roefs making a number of good saves.
Mitchell produced another all-action display and created a number of chances down the Palace left channel. But the Eagles had to settle for the draw, with the full-back looking to take the positives from the afternoon.
"We're frustrated. We wanted to win today. We wanted to get our first win at home, so we're disappointed, but if you don't win, don't lose.
"We put ourselves in good positions. The first-half shot we had, in the second half, we had a few chances.
"They've already pulled off well, so we're glad that our attackers are in the positions to be able to create chances and they \[will\] score goals."