Sidwell: Mourinho exit rocked Chelsea
"But we're such a big team, and we're in big competitions that we want to win. We didn't have time to sulk, so we had to get on with it."
A string of victories under Avram Grant helped stabilise the club as did the news that coach Steve Clarke was staying to work alongside Henk ten Cate, a new addition to Chelsea's coaching team.
Sidwell said: "The first thing was not to rock the boat too much. If you go in and change things round right away you can lose a few players and they don't know what they're doing.
"We haven't put ourselves in the best position with our start to the season but we've stuck together and made it through a tough patch and we can build on that.
"We know we've got work to do in the League but there's a long way to go and we're capable of doing it."