If Manchester City want to stay in the top four of the table and qualify for the Champions League, they will definitely have to win their upcoming matches consistently.
As already disccussed in this thread, due to being one of the two associations with the highest coefficient points from the three club competitions of the current season, England has been awarded and extra spot for the next season of champions league. Therefore, Manchester City (or any other team) can qualify for the champions league even finish the premier league at 5th place.