Warnock, signed from Aston Villa on a free transfer in January, kept his cool to ram home a 72nd-minute penalty after McCormack had seen his 28th-minute spot-kick turned on to a post by David Forde.
"I didn't want Ross to take the second penalty and put extra pressure on himself after missing the first," Warnock said. "I was going to send El-Hadji Diouf on to take it but Stephen wanted to take it straightaway and he told me he'd taken them before."
Leeds remain in the play-off hunt as a result of their eighth win in nine home league games, but now face a tricky week on the road that could prove crucial. Warnock added: "It was all about getting three points. It was a must-win before going away to Leicester and Crystal Palace and we deserved it, though we could have made it easier for ourselves."
McCormack's missed penalty came after Byram was needlessly brought down by Woolford 15 yards out on the right, while Scotland international McCormack also clipped a post with a chip-cross.
McCormack was also guilty of a poor first touch and tame shot from Luke Varney's cut-back but when the Scot was brought down by Alan Dunne inside the box, Warnock's powerful left-footed penalty gave Forde no chance.
"You have to really beat Millwall," Warnock said. "It`s a sort of game where you take a 1-0 win and get out of there."
Millwall manager Kenny Jackett had no complaints over the two penalty awards to Leeds but claimed the Lions should have had a spot-kick of their own.
He said: "My first impressions are that we couldn't complain about either of Leeds' penalties but I felt we had a clear-cut penalty when Danny Shittu headed the ball down, Sam Byram had his hand by the side of his body and clearly handled it as the ball was going through to my centre-forward, so I thought the referee got that call wrong.
"David Forde made a good save from the first penalty and he is in top form at present. We had big chances but Paddy Kenny pulled off two very good saves for them and Shane Lowry hooked one over from about seven yards, so we were unfortunate to come away with nothing."
- Sports & Recreation
- David Forde