The away side started as heavy favourites, given their position in the Premier League compared to League One side Wigan.
However, it was Wigan who once again got a big result in this competition against City.
"We knew a lot of things had to go right for you on the night against such a quality team," acknowledged Cook.
"The standard of football they play is at such an elite level.
"Every player handles the ball so comfortably, they work you so hard.
"We had to dig in, we really did, and the lads did that in abundance.
"Some of the blocks we made in the second half, we earned a little bit of luck.
"Griggy became very isolated in that second half, and that's great credit to Man City.
"It's so hard to play against, because they wear you down to such an extent and then they hurt you."