The defender struck the winner just after the hour mark, receiving the ball from Jack Grealish before curling into the far corner beyond Matt Turner with his weaker right foot.
Prior to the goal, the Gunners threatened on numerous occasions, with Stefan Ortega Moreno making two smart saves to keep the score level at the interval.
Ake, who won five duels, made three tackles and two clearances, was happy to see the team show determination, grit and resilience under the floodlights at the Etihad Stadium to secure passage into the fifth round.
“It’s good you know, especially after a tough period. It’s good to carry on and we take this as a tough opponent and to win 1-0 to go into the next round gives us confidence for the next game and the games to come.
“There’s more to come, today was about resilience, we stayed strong and made sure we didn’t concede, that’s what we need to show more of ourselves.
“The second half we were better, we played more our game. It was tough.
“Their press was high so it was difficult to play out.”
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The Dutchman, who was named as the Player of the Match after a match-winning display at both ends of the pitch, was also pleased to have got the goal to settle the tie.
“It was a good pass from Jack [Grealish],” he said.
“I think it’s the first one I’ve scored with my right, so I was pleased with that!”
