The Republic of Ireland right-back has confessed that the Goodison Park outfit are up against it to qualify for the Champions League.
Everton have suffered a number of negative results of late that have seen them lose ground in the race for a top-four finish.
Roberto Martinez’s charges sit in seventh place ahead of today’s crucial home game against West Ham, and trail Merseyside rivals Liverpool by 11 points.
"It's going to be very difficult now,” he told The Liverpool Echo.
"I'm really disappointed that we've faded off fourth a bit in the last couple of weeks.
"But personally I'm holding onto the dream even though I know it's difficult. We just need to keep going.
"We're still aiming to finish as high up the table as we can, and whether it's Champions League or Europa League, personally I'd like to play in Europe at some level and hopefully it can be next season.
"We've got the game in hand against Crystal Palace, which was annoying when that was called off but that's the way it goes."
Everton are locked on 45 points with Manchester United and are five behind Tottenham in fifth place.
Three points against a resurgent West Ham today would be a step in the right direction for Coleman and his side.