The league leaders saw their title advantage cut from 13 points during mid-March to just four at Old Trafford last Sunday.
The defeat was the second in four games for Antonio Conte’s men with unstoppable Spurs now in striking distance. Mauricio Pochettino’s side are also hoping to inflict a psychological blow by dumping Chelsea out of the FA Cup semi-finals this weekend.
But Cahill said: “That defeat has given us all a kick up the backside.
“We know the league is not over, that it will be difficult, but we know we are more than capable of doing it. I certainly think we can win our last six league games.
“We just need to come back from this now. We need to lean on the experience we have in the dressing room and the players that have been through all this before.
“We can’t let things get too twisted, after all we lost at Old Trafford which is a very tough place to go to.
“The most disappointing thing is we didn’t play to the levels we are used to or the levels we expect. It can happen. But that is why we were so angry in the dressing room afterwards.
“It is important we respond this week. We have to show the same response we did after losing to Crystal Palace, when we beat Manchester City and Bournemouth.
“Saturday will have nothing to do with the league. In my head, I don’t think it will have any impact. It is purely a cup game.
“Regardless of the opposition, we want to win it. We want to win the match because we want to pick up the FA Cup, it’s one of our goals. Anything else is irrelevant in my eyes.
“Are Tottenham now favourites? It’s a one-off game so however people want to build it up, they will.”
Chelsea are sweating on the fitness of keeper Thibaut Courtois and left wing-back Marcos Alonso, both of whom took no part in the defeat at United.
Conte is also concerned by Diego Costa’s mini-goal drought – the striker has not scored in the league since March 6 – and the dip in form of several other players.
Cahill, however, insisted his side will defy the doubters. He added: “We will be in training for the majority of this week, preparing and recovering. There are two aspects to the current situation and what we do.
“The first is a positive: we are still in a great position and have six games left to play.
“The negative is: no one will give us this league. We are not going to get the trophy just because we have done well for the majority of the season. We have six games left and have to earn the right to win it. No one is going to roll over.”