Injury-hit United went into the match with a makeshift defence, including regular midfielders Antonio Valencia and Daley Blind, on the back of three successive Premier League matches without victory.
The breakthrough eventually came 23 minutes from the end as Palace goalkeeper Julian Speroni failed to keep out Juan Mata's deflected effort, but Warnock was left ruing what might have been.
Fraizer Campbell almost put Palace ahead just before half-time as the hosts struggled to make the most of their larger share of possession and Warnock felt things could have been far different had the former United striker found the target.
He said: "That was my best opportunity to beat Man United if I'm honest, what with the run they are going through.
"I think the chance, the best chance of the game, for Fraizer Campbell, that was the one opportunity. It would have put a lot more pressure on the side then because they’re expected to beat Crystal Palace, aren't they?
"I thought we were solid again. It was nice to see us not being gung-ho like in the last few weeks.
"I don't think Julian had much to do if I'm honest. But it's all about taking your opportunities and I don't think we'll have a better one than that at Old Trafford or anywhere else really.
"Julian will probably be a bit disappointed, but he's saved us that many times over the years and it did take a slight deflection.
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