Victory over Cardiff on Saturday, combined with Manchester United's defeat against Liverpool, moved the Toffees back into sixth place and the final qualifying spot for European football.
The Champions League looks to be out of reach now with fourth-placed Manchester City nine points ahead with a match in hand but the second-tier competition is a realistic possibility.
Everton's squad, which currently has four loan players in it, is small and any European campaign could prove detrimental but Distin insists they would accept that if they are successful.
"It's mixed feelings because you can't say no to playing in Europe. As a player it's impossible to not want that," he told the Liverpool Echo.
"But it's completely different from the Champions League in terms of finances for the club. It's a lot of travel and you need a big squad.
"Yes, it would be amazing for the club and for the fans to be travelling back in Europe again but for the team, if we're not going to have a much bigger squad next season, it could be tough.
"If you look at the big picture, as I say it's important you've got to ensure that being in the Europa League doesn't make you suffer back in the league.
"When you play every Thursday and come back on the Friday before playing again on the Sunday it is hard."
Distin stressed, however, they have not yet given up hope of a top-four finish.
"As long as it is mathematically possible we will try, we will not give up," he told evertontv.
"We have 10 games left and will try to finish as high as we can."