Dzeko is all too familiar with the surprises that England's top flight can spring, as he spent five years of his career playing for Manchester City before moving to Roma last year.
"That's the English Premier League. You can win against the best teams and then lose against the last," the London Evening Standard quotes the forward as saying.
"Chelsea is a great team with some amazing players. Wednesday will be a much different game and will be much more difficult for us than it was for Crystal Palace, even though they won the game.
"We'll play maybe also against an angry, but top team. Their coach will put pressure on them, but we didn't come here to play and lose, we came here to give our best and have a positive result."
Roma currently sit second in Group C, two points adrift of leaders Chelsea.