Yaya Toure set City on their way and a controversial Sergio Aguero penalty doubled the lead before half-time.
Carlos Tevez and Aguero were on target after the break as the npower Championship visitors were swept aside.
Warnock admitted his side were second best but felt aggrieved that referee Mark Clattenburg called for a penalty after an innocuous tug by Lees on Aguero in the box.
"I know Mark sees it differently and he's had a good game today [Sunday] but he wouldn't give a foul anywhere else on the pitch," said Warnock.
"The lad is clever the way he appeals but it's such a soft penalty.
""And so we're 2-0 down after 14 minutes. You think the worst but I think they've done really well.
"We have had great cup runs this season but I think in the first 10 minutes the young lads were a little bit overawed. But we hung in there and I was quite pleased they didn't fold.
"The second goal is vital when they're desperate to get a result but it's never a penalty in a million years.
"Let's be fair, they were still better than us but it made it easier for them."
Warnock is coming under increasing pressure from the fans to quit having failed to mastermind a promotion challenge, and cries of 'Warnock - time to go' were the printable catcalls aimed at him from the away end.
His contract is up at the end of the season and he has told owners GFH Capital he will not be staying on next season, while he claimed he would leave earlier if he was asked.
"I don't deserve that (abuse) after the year I have had, but I am unlucky to have been at three clubs with three takeovers,"he said, referencing previous spells with Crystal Palace and QPR.
"I understand their feelings and the noise they make shows what sort of club it is.
"If we go up, the owners know I won't be here and the further away we get (from promotion) the club will be looking to see what they're going to do and, if I can, I will help them."
Warnock took over at Elland Road a year ago and after a passionate start where he engaged with the supporters and got them onside, he now accepts the writing is on the wall as far as his pursuit of a record eighth promotion goes.
"I'm living away from home for one last year at promotion," he said.
"I'm sure the club will be sensible and in a couple of years they will be back in the big time.
"It's their prerogative (if they want to sack him), if they think it will help, I'm not against it. Whatever is best for Leeds United. But with what's gone on over the last 12 months I think I deserve a medal."
City were widely criticised for a lacklustre at St Mary's last time out but they were far too strong for Leeds as they eased into the quarter-finals.
And James Milner was delighted with the way Manchester City bounced back from their setback at Southampton last weekend with a convincing 4-0 FA Cup defeat of Leeds.
Milner, playing against the club who handed him a league debut in 2002, told ESPN: "I hadn't played against them before but once you get on the field it's just another game. It was a good atmosphere and a good result for us in the end.
"It was important we bounced back, they've knocked a few Premier League teams out of cups this season so it was important we did a job and we did it well.
"We had to improve on last week, we did that, we kept a clean sheet and scored four goals so that's pleasing."
Toure added: "We know Leeds are a very tough team.
"They play very good football and are physically strong. Today [Sunday] was a good response from Man City."