Warnock pinpointed the loss of centre-back Claude Davis to injury in the 56th minute as the turning point in the game.
The former Sheffield United boss said: "I thought it was there to win and we've ended up losing it, but I thought as soon as Claude Davis went off we got back to old ways.
"I thought that was the difference. When he was on we were comfortable but when he came off we were a good 20 yards deeper and invited more pressure.
"But if Victor Moses or Clint Hill had scored and not hit the post I think we would have been comfortable.
"The first goal was always going to win it. I thought we should have stepped up a gear and tried to win, but that's something we're obviously not capable of."
Owls boss Brian Laws was relieved to avoid three defeats in a row
"It wasn't about our performance today - it was about getting the win and avoiding a third straight defeat. That was the key.
"Even before the game, our back four was put together with some glue, sellotape and sticky back plastic.
"Richard Wood had to pull out before the game because he wasn't fit and we were very, very stretched.
"I had to put Frank Simek in the side and he's only played 70 minutes in a year.
"That's credit to him, and Richard Hinds has had to play a second game when he should never have been anywhere near the side.
"But I thought they were magnificent."