The Toffees matched their score from the first leg by recording a 1-0 win in Slovakia thanks to substitute Dominic Calvert-Lewin. The striker came off the bench to make the difference for Ronald Koeman's side, who had again looked ponderous and disjointed, with a composed finish 10 minutes from time.
The result meant that Everton won the tie 2-0 on aggregate and are in the "hat" for tomorrow's draw but the manager knows his charges must keep improving before the Premier League season kicks off in a little over a week's time.
“I think we were better defensively tonight than we were last week,” Koeman told evertonfc.com. “But we know that we can and need to improve in our ball possession. We had a lot of space for one of the two centre-backs in the first half and we need to dribble in and create more than we did.
"It was a really physical game and 90 minutes that the players need in pre-season. We are through to the next round, the job is done and I'm really happy.
"The Europa League has always been important for me. I like to be in Europe - it's important for our experience. It's good for the club, the players and the fans. It's not easy to reach the group stages but we will do everything to get there.”