United's main aim is to catch Hearts for third spot and Levein has told his players he expects his former club to win Thursday's Edinburgh derby so a victory over Aberdeen is crucial.
With two European places up for grabs, United could find themselves in a commanding position on Thursday night but their manager believes the race for Europe would be far from over.
He said: "A win against Aberdeen would take us a significant step towards European football but it wouldn't seal it.
"There would be a seven-point gap but with nine to play for, so we're not looking towards it like that.
"All we're concentrating on is winning the game to stay ahead of Aberdeen and keep the pressure on Hearts.
"I think they'll beat Hibs in the Edinburgh derby because Hibs have a lot of injuries, so we need to win over Aberdeen to keep things going.
"I expect ours to be a very good game because we've both reached the stage where a point is not really enough.
"As I said, I think we need to win to stay in touch with Hearts, while Jimmy Calderwood will look at it and say a point is not much use.
"Therefore, I think we're going to get a really open match between both teams, who are at the top of their games."
Levein has been hit by injuries to top scorer Francisco Sandaza and Northern Ireland international Warren Feeney.
That means he will have to call upon David Goodwillie and Andis Shala but he is backing the two youngsters to shine.
Goodwillie scored the winner against Hibs last weekend and is a player Levein feels is ready to step into the limelight.
He said: "Andis and Goodie are both young but they've played together a lot in the reserves this season, so they know each other's game.
"Goodie is a talented player and his ability has never been in question.
"What he had to do was focus and I think he's done that over the last year.
"As for Andis, he's more raw and inexperienced but he's got a presence which defenders find intimidating."
In addition to Feeney and Sandaza, United skipper Lee Wilkie is banned but Paul Dixon returns after suspension.
Levein has confirmed his interest in Slovakian keeper Dusan Pernis but admits the player's contract with MSK Zilina presents a problem.
The 24-year-old is tied up until January but United want their new man in for pre-season so are likely to look at alternatives, with ex-Valencia man Alberto Marrama high on their list.
Levein said: "Dusan is one of several players we're looking and and he's a good keeper.
"But he's contracted to his club until next year so he's probably the least likely option at the moment."