Evans was heavily linked with City in the closing weeks of the transfer window as Pep Guardiola looked to strengthen his defensive options, but West Brom were able to fend off that attention and hang onto their captain.
Throughout the chase Tony Pulis was adamant Evans would remain at The Hawthorns, but had conceded an "enormous offer" could make them reconsider.
That never came and interest from Arsenal also failed to materialise as Albion got their way.
"In the back of my mind I've always been thinking 'whatever happens, happens' and just got on with it," Evans told Sky Sports News.
"I think I'm quite strong mentally, over the years you learn to deal with things as a footballer, just concentrate on your football.
"The most important thing for me really was that I was fit for the game and trying to deal with that side of it.
"Obviously the window closes the day before the game [so] it's not ideal. The game came at the right time."
Evans has not featured for West Brom this season due to his injury but he made his return on Friday as Northern Ireland picked up a 3-0 win to remain second behind Germany in Group C.
The 29-year-old played the full 90 minutes as three goals in eight minutes secured the three points, keeping them seven clear of Czech Republic - who they face on Monday - in third.
"It obviously wasn't the most physical match, we had a lot of the ball so it was a nice one to come back into," he added.
"I haven't done much, maybe last weekend was the first time I'd done a hard session.
"Then throughout the week you're sort of being cautious because there are that many injuries in the squad that we didn't want to push it and have myself out for the game."