Morgan Schneiderlin has pleaded with his teammates to continue fighting for the shirt.
The Toffees lost 4-0 to Manchester United on Sunday, which followed an embarrassing 3-0 lost to Atalanta during the week.
"Of course [we felt like we were in the game up until the second goal]," he said.
"We knew that coming to Old Trafford, we had to keep good possession of the ball and then we could create some chances. Wayne [Rooney] went close right at the start of the second half and then Gylfi [Sigurdsson] had a chance in the second half, too. We could have scored and got it back to 1-1 but we didn't do that.
"We have to take the positives after our performance compared to Thursday, which was horrendous from our point of view. We knew before the game we had to find the fighting spirit that we lacked in the past couple of games.
"It was a case of showing our fans that we are here, that we fight for the ball and fight for the shirt. I think we showed that for a long period of time but we can't make the mistakes we did because you get punished.
"Yes, we're disappointed and nobody wants to lose 4-0 but whether it's 2-0 or 4-0, it's still a defeat. We found some aggression back today and we need to look forward to the next game."