"I think it's going to come down to the wire. There are still three tough games for both of us ahead and we'll give it our all and hopefully we can sneak in there," said Coleman, according to The Herald.
"We just move on now, finish the season strong and hopefully get that fourth spot.
"Obviously, we had a disappointment midweek against Palace, so yesterday was probably a must win game."
Everton currently sit in fifth position in the Premier League table, one point behind fourth-placed Arsenal.