The Citizens followed up last season's trophiless campaign with two major honours this time around, adding the Premier League and EFL Cup to their collection.
Walker, a top-flight title winner for the first time, has played a key part in City's success with his displays down the right-hand side.
Far from being the complete package, though, the England international claims that the 5-1 aggregate defeat to Liverpool last week proves there is far more to come.
"There is still a lot of room for improvement," he told BBC Sport. "I have read some articles that say we need to win things continuously for a number of years before we are classed as a great team.
"Every single one of us wants to be recognised as one of the greatest teams to play in the Premier League. If we concentrate on ourselves then as a team we can go on to great things. But the Liverpool game showed us that we are not a perfect team.
"Different managers have different ways of looking at things and the gaffer here is special. He has won everything you want to win. Bar three people in the dressing room, no-one has won the Champions League. He has done it on a number of occasions so you have to buy into his philosophy and his way of playing."
Walker joined City from Tottenham Hotspur in a £45m deal last July.