Though they are only one point off the fourth place that would get them into the competition's qualifying round, their final six matches include a visit to leaders Bayern Munich next week as well as a clash with fifth-placed Bayer Leverkusen.
"We know we have to do everything better against Dortmund," said Cameroon forward Eric-Maxim Choupo-Moting. "We need to be there 100 percent both mentally and physically ... We cannot allow mistakes because Dortmund will punish us."
To make matters worse for Schalke's fans, Dortmund, who beat the Royal Blues 3-2 earlier in the season, made sure of at least second place last week, and are still in the race for three titles.
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They have not only outscored league leaders Bayern, but have also amassed a points total - 67 - that would have made them league leaders at this stage in 49 of the last 52 seasons.
"We all hope we can reach (that level)," said Breitenreiter. "At the moment, though, we are a long way from that. You need time and patience to form a hungry team, to constantly play at the top level and compete for titles."
Schalke's injured midfielder Leon Goretzka is unavailable while Klaas-Jan Huntelaar, benched for the past two matches, could start instead of misfiring fellow forward Franco Di Santo.
Also vying for the remaining Champions League places are Hertha Berlin, on 48 points, Borussia Moenchengladbach and Bayer Leverkusen on 45, and Mainz 05, level with Schalke on 44.
Bayern, top of the table on 72 points, travel to VfB Stuttgart on Saturday while Hertha will look to recover from last week's 5-0 demolition by Gladbach with a win over basement side Hanover 96.
(Reporting by Karolos Grohmann; Editing by Kevin Liffey)
