The Dons took great credit from their Scottish Cup semifinal performance as they faced the heartbreak of losing on penalties on Saturday.
Interim boss Leven wants their Hampden display to be the benchmark and is looking for a clean sweep of five wins in the bottom six.
Ninth-placed Dons start with Motherwell this weekend, then take on St Johnstone, Hibs, Livingston before finally Ross County away.
Leven said: "The challenge is to finish as high up the table as possible.
"I said to them, 'We go to the league and finish as high as we can, that is the challenge'.
It's going to be a big push until the end of the season. We have to give more of the same. We are in a position where we don't want to be.
"We have five massive games, starting on Saturday.
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Denne historien er fra April 23, 2024-utgaven av Daily Record.
Start din 7-dagers gratis prøveperiode på Magzter GOLD for å få tilgang til tusenvis av utvalgte premiumhistorier og 9000+ magasiner og aviser.
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