The Toffees kept the pressure on fourth-placed Arsenal by winning this afternoon to remain one point adrift of the Gunners in the race for Champions League qualification.
"We wanted to respond and show that we had that grit and we showed that today," he told BBC Sport.
The visit of the reigning Premier League champions saw the return of former Everton boss David Moyes, and the left-back says that his presence added spice to the fixture.
"I think it (Moyes coming back) did (add extra spice to the game) for the fans," he added. "It meant a lot for them and the victory was for them as we let them down in midweek by losing to Crystal Palace."
First-half goals from Baines and Kevin Mirallas proved enough to down the Red Devils.