Levein, who managed Scotland for three years, said the loan signing of Duffy from Premier League outfit Brighton 'does not make sense.'
Duffy, 28, is a lifelong Celtic fan and was desperate to seal his move to the Scottish champions last summer.
His arrival at Parkhead delighted many Celtic supporters but the Ireland captain has struggled to find his best form in Lennon's team and he has failed to start Celtic's last three matches.
The Hoops have won just two of their last 10 matches in all competitions and sit 11 points behind Rangers at the top of the Premiership, albeit with two games in hand, as they bid for their 10th straight title.
They are also out of the Europa League with two group games remaining.
Even Lennon admitted he feared the sack after Celtic's 2-0 League Cup home loss to Ross County.
“Shane Duffy is a really, really good player,” Levein said.
“But he played in a Brighton team that defended deep. Celtic’s defence are always going to be close to the halfway line.
"Celtic’s centre-backs have to be able to run. They have to be quick. Shane Duffy doesn’t fit what Celtic do, he’s very good, but it doesn’t make sense to me.”
Meanwhile, Duffy will have a knee injury assessed ahead of Celtic’s Europa League clash with AC Mlilan in Italy on Thursday night.
Fellow defender Christopher Jullien has played two games after a long spell out injured with a back problem and is a doubt.
Attacker Mohamed Elyounoussi will not be available through injury and James Forrest remains sidelined after ankle surgery, but defender Jeremie Frimpong returns after being suspended for the cup defeat by Ross County at the weekend.
Lennon admits he would have understood if Sunday’s defeat had ended his reign as Celtic boss.
The Northern Irishman came under increasing pressure following the 2-0 loss which saw hundreds of fans turn up at Parkhead afterwards to demand the removal of their manager, amid scenes of chaos as police tried to keep order.
Asked if he thought in his heart of hearts that it was over for him on Sunday, the former Celtic captain, in his second spell as Parkhead boss, said: “Not in my heart of hearts, but I could understand if that would have been the case, yes.
“I am very grateful (for the board’s backing). They are not a board that sack managers for the sake of it.
“We have had great success, we are going through a tough time but they don’t leave you out in the lurch.
“There is great support here. Great support from supporters, letters, emails, there has been great support from other managers in the game, and the LMA (League Managers Association) who have seen it all before and who probably deal with it on a daily basis.
“It is really encouraging and comforting and I have had great support from the players as well.
“From my own point of view, for 20 years I have done everything in my power to bring success to the club and the fans.
“That is not going to change on the run of a bad month or people being upset by my style of management if they want to say that.
“I owe it to the players, they are working hard to turn it around and they are feeling it at the minute so they need my support as well.”