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.
This story is from the April 23, 2024 edition of Daily Record.
Start your 7-day Magzter GOLD free trial to access thousands of curated premium stories, and 8,500+ magazines and newspapers.
Already a subscriber ? Sign In
This story is from the April 23, 2024 edition of Daily Record.
Start your 7-day Magzter GOLD free trial to access thousands of curated premium stories, and 8,500+ magazines and newspapers.
Already a subscriber? Sign In
MY DAYS ARE NUMBERED
Morgan: I've followed Forrest's formula to success and put focus on efficiency
KEEP IT TO YOURSELF
Remi: Caley Thistle won't worry what survival rivals do
UP THE GREEK
Kaabi takes Villa for ride as Euro bid is derailed
I'LL BE BACK
Higgins vows to make return to the Crucible
I knew Nora was going but I was like, no way
Johnny Rotten's tears on tour as he recalls death of beloved wife Catch more that
CARER STOLE £5K
Hospital worker took dementia patient's bank card
Thank you for saving our Caleb
Dad praises hospital team as son recovers from surgery to remove malignant tumour
I'VE GNAW IDEA HOW I GOT HERE
Mystery as animal team is called to rescue roaming rodent from beach
E-scooters on Scots roads is 'inevitable'
Hyslop adamant despite 'problematic' safety
GET OFF THE PLANE YA PAIR OF EGYPTS
Holidaymakers chant cheerio as yobs led off