City claimed the league title with five games remaining on Sunday, following a shock Manchester United defeat by West Brom. City currently have 87 points this season, 16 ahead of Mourinho's side.
Speaking to 'BBC Radio 5 Live', Walker admitted: ''There is still a lot of room for improvement. 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.''
He added: ''Everyone 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.''
Guardiola led Barcelona to two Champions League titles, and La Liga three times, whilst at Bayern Munich he claimed the Bundesliga title three times.
Walker said of his manager: ''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.''
The 27-year-old also noted that Guardiola's attitude on and off the pitch is admired and respected by the club. Walker revealed that the Spaniard operates an open door policy and puts his heart and soul into City.
He said: ''Before you go on the pitch, he makes you feel like you are the best player on the field. His emotions do run away from themselves sometimes and he knows that, but I would not change that for any other way because I know he is passionate about his job.''