Carvalho said: "It was a very important win, we were five points behind Manchester United and knew we had to do our job. Now we have to wait to see what they do. We knew we couldn't make a mistake against Everton and had to win, we have done that and now the gap is only two points. The pressure is back on them.
"We will have to beat them as well, but we will have to see first how they get on against Blackburn on Saturday. Blackburn away is always difficult.
"We showed a lot of character and showed how strong we are after drawing against Wigan. This was a crucial game for us.
"We knew we couldn't draw or lose again. We have to win every game.
"It will be difficult for us to win the league but it is still possible. But we will never give up and it is important we beat Manchester United, even though that will be hard."
The Portuguese international defender is now fully focussed on beating Liverpool in the semi-final of the Champion League.
He has played in both of Chelsea's defeats to Rafael Benitez's men at the same stage twice in the last three years.
He said: "The Champions League is very important for us and has been since I joined the club.
"The first leg at Anfield will be crucial and I hope the luck is on our side this time."