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.
Rotherham produced some decent football at times, but also played themselves into trouble on too many occasions.
"We try to be a team and so far we have done incredible with results". Fifty points is incredible, it is huge.
"But they are an opponent that has done better than us without him", 47-year-old Guardiola insisted, before adding.
"Last season he played incredible minutes but hopefully in the second leg of the season he will help us because we need him. Today he was our captain and he showed us why".
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.
"We took (it) seriously", said Guardiola.
Sterling has grown to become a key player for club and country in the last few years.
'The great clubs don't choose competitions, don't choose games.
"Danilo deserved to play and played well against Southampton, and today Kyle played best game of the season by far".
"Have to do our job, and we did it amazingly again".
England worldwide Sterling was City's brightest light with the forward's pace and direct running causing Paul Warne's side problems throughout. We created a lot of chances (against Rotherham) but if we play against Liverpool or in the Champions League we create just two or three chances. "It summed it up when I told my right-back (Zac Vyner) to smile when (Raheem) Sterling came off and (Leroy) Sane came on".
"I think he improved a lot and it's the same with Phil [Foden]".