A 9-2 aggregate defeat to Real Madrid brought an emphatic end to their Champions League campaign, but they are keen to return again next season.
Having moved up from seventh at the turn of the year to third, three points clear of Bayer Leverkusen, they now intend to cement their place inside the top three with a win over bottom club Eintracht Braunschweig this Saturday - and not suffer a Champions League hangover.
Coach Jens Keller said: "Our coming challenges are all very significant, which is why it would be very important to win them.
"That's not to say anything will be decided in them - it's going to be exciting right to the end."
After hosting Braunschweig, Schalke travel to local rivals Borussia Dortmund in midweek, which is why picking up three points is particularly important against the league strugglers.
"We're at home and, given our individual quality, we've really got to win," added Keller, who is without his captain Benedikt Howedes due to a groin strain.
"That's catastrophic for Bene and for us," said Keller, who is likely to be without the German central defender for several weeks.
Keller also has a doubt over the fitness of Jefferson Farfan due to a knee injury.
While many Schalke players savoured the occasion of playing at the Estadio Santiago Bernabeu in midweek, for much of the Braunschweig team, a visit to the Arena AufSchalke is comparable.
"I've never been there and to be able to experience this atmosphere is a privilege that we want to be able to enjoy again next season," said visiting coach Torsten Lieberknecht at a press conference.
"Schalke are favourites and we're outsiders, but we still want to win."
Braunschweig are currently four points adrift of safety at the foot of the Bundesliga.