Striker Victor Anichebe says it would be a failure if Everton do not qualify for Europe this season.
The 21-year-old forward scored his first goal since returning from a 12-month injury lay-off during the Toffees' 2-2 draw with Birmingham at the weekend.
David Moyes' side had taken a two-goal lead at St Andrews but were pegged back and only left with a point.
Everton are currently ninth in the Premier League table with 42 points from 29 games and face a race to finish in the Europa League places.
Anichebe said: "It would feel like a failure to not qualify for Europe. We all really want that.
"The amount of players we've had it has been hard, and it's a credit to the boys that we are this far up the league considering that we've been missing big players.
"It's a real testament to us, but we've still got hope.
"We've got nine games left and an okay run-in so we need to just keep pushing. There is still belief we can get into Europe."
A win on Saturday would have put Everton above Birmingham and Anichebe knows they should have secured the three points.
He added: "It was frustrating. We were on top for so long and then they got a fortunate goal, and it spurred them and the crowd on to believe they could get back into it.
"They did put us under a lot of pressure and were up for it. It's a very hard place to come to. It's like when teams come to Goodison, and they do find it hard.
"I would like to think we are a lot better than them, but they play to their strengths and they are doing well in the league. When it's 2-0 we need to maybe just sit back a bit and be a bit steadier. When they got a goal back it made things very difficult.
"They will all be hard games left. But if we show enough character and play as well as we did in spells against Birmingham then we should finish in a good position."
The young forward also thinks he will have to continue to fight for his place in the team, despite the imminent departure of Landon Donovan.
"The team is flexible," he remarked. "Just because Landon is going doesn't mean I'll automatically be starting in there. I will keep fighting for my place."