The Tannadice boss took his players to the Irn-Bru Second Division side's ground on Monday morning for a training session to get them used to the surface.
While Levein would always want to play his first-team matches on grass, he knows this is not possible in the modern era and praised Alloa's state-of-the-art set-up.
The former Hearts and Leicester manager will leave out Andy Webster, who is carrying a knock, and Danny Swanson for the second-round tie, but insists the rest of his players will have no problem adapting.
He said: "The surface is good and we've no worries about playing on it.
"Obviously nothing will be as good as grass but these artificial pitches are being developed to become better all the time.
"People used to look at them and think they were dangerous but I don't think that's the case now.
"The other thing is, we have a young squad and most of the lads have played on plastic regularly over the years so are used to it.
"We do have a few players who won't play on it, I don't think it suits Danny Swanson and Andy Webster has had a wee niggle so we'll leave him out.
"Steve Banks will come in to play in goal as well and I've got a few decisions to make on my strikers."
Levein, who will choose between Andis Shala, Johnny Russell, David Goodwillie and new signing Damian Casalinuovo in attack, is mindful this stage of the cup often produces shock results, so will be doing his best to ensure his players are properly focused.
United got to the final of the competition two seasons ago and would dearly love to return to the glamour of Hampden, but in order to do so Levein knows they must first complete their work on the smaller stage.
He said: "In this round of the cup there are always teams who get knocked out so we have to be wary of that.
"And although I am making changes it's not as though I'll be bringing in anyone who is untried.
"We have a fairly big squad and a lot of quality players so this will maybe be a chance for some of the lads who have not been playing so far.
"But everyone will be first-team players and the folk who do come in will be desperate to play because they'll want to use the opportunity to impress."