Everton defender James Tarkowski praised the support after defeat at home to Manchester City.
The Blues lost 3-0 at Goodison Park on Sunday.
Tarkowski said, "I thought we were in it till they scored their first goal. We felt good and were countering well. It was pleasing to a point, but we always knew it would be a tough day. We needed a bit of luck but it just didn't go our way.
"It was a terrific finish [for City's first goal], but we're more worried about how the ball got there. They're a top side and once they're in the final third, if you don't get those little details right they'll score.
"You saw by the fans' reaction [at the end]. They stuck by us and they've been incredible. We've got every belief [we'll avoid relegation] and this won't knock us back."