The defeat at Old Trafford was Chelsea's second in four games, which has allowed Tottenham to close the gap on the league leaders to only four points.
"That defeat has given us all a kick up the backside," Cahill told Standard Sport.
"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 can't let things get too twisted."
Chelsea's remaining Premier League games are against Watford, Southampton, Everton, Middlesbrough, West Brom, and Sunderland. Only the Everton and West Brom ties are away from Stamford Bridge.
"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," Cahill added.
"We are not going to get the trophy just because we have done well for the majority of the season... We need to work hard in training and go again. But we must also remember we are still in a strong position."