The Africa Cup of Nations has denied Chelsea of the services of Didier Drogba, Michael Essien, Salomon Kalou and John Obi Mikel over recent weeks, while John Terry and Frank Lampard have also been absent through injury.
"We have not slipped up even though everyone expected us to fail because of injuries and the Africa Cup of Nations," Carvalho told the Daily Express.
"But we've not missed a single chance in the competitions. It is a big time for us.
"We knew January was always going to be important but we have shown our determination by coming through it.
"But we have shown we do not just rely on players like Lampard, Terry, Essien and Drogba. Other players have a big part to play.
"We have come through complicated situations in the past because of injuries and we can do it again."