Celtic fell six points behind cinch Premiership leaders Rangers at the weekend after being held to a 1-1 home draw by Dundee United. Ange Postecoglou's side sit sixth after seven matches and have dropped more points than they have gained.
The new manager has been severely hampered by injuries with 10 players missing by the time the second half kicked off on Sunday.
Levein also feels the long-term absence of centre-back Christopher Jullien continues to be a major blow with summer signings Carl Starfelt and Cameron Carter-Vickers still to convince. The Frenchman is in the latter stages of his rehab following knee surgery.
When asked if Celtic had the squad to mount a sustained challenge, Levein told BBC Radio Scotland's Sportsound programme: "At this moment in time, no, because a lot of players that they would need to do that are on the treatment table. So that's a simple no.
"And also, if they don't get Jullien back in the team as soon as possible, I think they will continue to struggle, because he is the one with pace and athleticism that can do exactly what the manager wants him to do."
Analysing Celtic's draw with United, the former Tannadice manager said: "They had some good chances, played some good football and I don't think anyone could criticise Ange Postecoglou for his attempts to play good football.
"But the one criticism I would level at Celtic is the inability to defend properly.
"It's a very risky way of playing for your centre-backs because they are left exposed at times. If that's the case, you need to be able to run, you need to be quick and be able to cover anything that goes in behind.
"I'm just not 100 per cent sure they have the centre-backs that are required to play that way."
James McCarthy and Josip Juranovic added to Postecoglou's injury woes during the first half on Sunday with Greg Taylor, James Forrest, Karamoko Dembele, Mikey Johnston and recent arrival Giorgos Giakoumakis also out.
The only attacking option Postecoglou had on the bench was untried 19-year-old Owen Moffat.
Although expressing sympathy for Postecoglou's misfortune, Levein expects a Celtic squad should have the depth to deal with injury situations.
He added: "If you go back to when Brendan Rodgers was in charge of Celtic, and look at the team he had and look at the team Ange Postecoglou has, it's night and day. It really is.
"I don't think Celtic have recruited very well at all. A team the size of Celtic should have strength in depth.
"I understand completely the manager has just arrived and hasn't had a lot of time to bring in the players required.
"So it might just be that the Celtic supporters need to suffer for the time being and hope they get things right in January."