Rotherham’s first visit to the Etihad Stadium proved a sobering one as Pep Guardiola’s men ran riot, the margin of Cup defeat eclipsing the Millers’ 6-0 loss to Brighton in February, 1960.
The Millers have not won a tie in the competition since beating Yorkshire rivals Bradford City in November 2013.
The win represented the first time that City – who led 3-0 at half-time – have scored seven in an FA Cup tie since 1968.
Warne, whose side face a Championship relegation six-pointer at Ipswich Town on Saturday, said: “We said to the lads beforehand that there was no pressure, but there will be next week.
“The lads will not be too disheartened by the scoreline. I know it sounds depressing, but Premier League teams come here and get a good licking. We should not be embarrassed about that, it was just that the gulf in class was so great.
“I spoke to Pep briefly before the game and said, ‘be gentle’ on the side of the pitch and then after I just shook his hand and said, ‘your team is a joy to watch.’
“A pain to watch would have been more polite.”
Approaching the interval the Millers only trailed 1-0 before a strike from Phil Foden and a Semi Ajayi own goal ended the game as a competitive entity and Warne admits that the second half was all about attempted damage limitation.
Warne, who had only six substitutes, added: “At half-time it felt more like damage limitation than realism.
“Can I ask my lads to give me much more? No, I cannot. The gulf in class was there for everyone to see. It summed it up when I told my right-back (Zac Vyner) to smile when (Raheem) Sterling came off and (Leroy) Sane came on.”