The Russian billionaire turned on the Chelsea squad after firing Andre Villas-Boas on Sunday.
Mata said: "I don't know if the players are playing for their future. But we have to prove ourselves every game.
"For me and the other players, we are playing in a top squad and for a top club — and we must always do our best in every game.
"Roman told us that we have an opportunity to change this run of defeats. Against Birmingham, we did so we have to keep going and try to get better."