The Blues were forced to settle for a goalless draw with title rivals Arsenal at Stamford Bridge on Sunday just days after Chelsea eased to a 6-0 victory over Qarabag in the Champions League.
The title holders lost 3-2 to Burnley in their season opener before bouncing back with successive victories over Tottenham Hotspur, Everton and Leicester City.
Chelsea moved back to within a point of Manchester City and Manchester United thanks to their winning run before falling further behind this weekend.
Antonio Conte made wholesale changes for the visit of Qarabag on Wednesday night as the Italian coach looks to win the Champions League for the first time.
Former Spurs legend Crooks has questioned whether Chelsea are capable of coping with battling on two different fronts this season.
“That is an important point, because if Chelsea intend to progress in the Champions League, and be serious contenders to retain the title, then more of their players are going to have to deal with playing in midweek and picking up valuable points in the league at the same time,” Crooks told BBC Sport.
“Manchester City have proved they are capable of producing victories after Champions League fixtures, and have the appetite to score goals. Arsenal played in the Europa League two days after Chelsea’s European game yet somehow looked better for it.”
Chelsea won the Premier League title with two games to spare last season in their first campaign under Conte.
The Blues signed six players in the summer transfer window to improve their squad depth.
The west London side will host Nottingham Forest in the League Cup on Wednesday night.
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