The champions lost 2-1 at West Ham United on Saturday, their fifth defeat in 10 league matches, and are labouring in 15th place in the table, a point behind Stoke.
A Stoke home win in Tuesday's League Cup clash would add to Chelsea boss Jose Mourinho's problems, after he was hit with a misconduct charge by the FA after being sent to the stands for comments to the referee at Upton Park on Saturday.
All kinds of theories have been put forward as to why Chelsea are struggling so badly with a lack of summer strengthening, a sudden inability to defend and Mourinho losing support in the dressing room among the favourites.
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Yet Begovic, who joined Chelsea to replace long-standing keeper Petr Cech who was allowed to join London rivals Arsenal, says the problems are being exaggerated.
"It's coming from all corners at the moment so we have to cope with that," Begovic said of the West Ham setback in which Chelsea played half the match with 10 men after Nemanja Matic was shown two yellow cards.
"We came back, we showed good character and I think our performance showed we are still positive and trying hard, it's just that little moments are not going our way."
Chelsea's terrible start in the Premier League means their League Cup clash at Stoke has suddenly grown in importance. Defeat for the holders would prompt another load of unwanted headlines predicting Mourinho's downfall.
Yet, despite his side being so far off the pace, Begovic says writing off Chelsea as a force this season would be a mistake for their rivals.
"We're going to take it a game at a time -- there is still a long way to go," he told the club's website.
"This league is very unpredictable so we need to take care of our performances first -- I think our performances are getting better so we just need to keep that going."
(Reporting by Martyn Herman; Editing by Mark Lamport-Stokes)
