The Citizens bowed out to Liverpool in the quarter-finals of the Champions League courtesy of defeats both home and away, and also lost 3-2 to Manchester United in the Premier League at the Etihad Stadium.
City returned to winning ways against Tottenham Hotspur on Saturday night, however, before being confirmed as Premier League champions for the 2017-18 campaign when United lost at home to West Bromwich Albion on Sunday afternoon.
"We've had probably the toughest period, definitely in my career at the club. We've gone from doing so well in all competitions to take three losses, and sometimes it felt like it was a relegation battle in there with the mood," Walker told reporters.
"We're all winners and we want to win and in those games unfortunately we didn't. But we put that right. That shows the character and the belief in the standard of players in the dressing room."
City's first match as confirmed champions will be at home to struggling Swansea City this weekend.