Massimiliano Allegri's side succumbed to a shock 2-1 defeat at the Allianz Stadium against the Red Devils , despite taking the lead through a sumptuous second-half Cristiano Ronaldo volley.
Juan Mata fired home a trademark free kick with four minutes to go, before an Alex Sandro own goal three minutes later secured all three points for the visitors.
Ex-United midfielder Scholes felt that Szczesny failed to adequately deal with Ashley Young's ball in which ultimately led to the winner and he believes that the 28-year-old is Juve's achilles heel.
"I think that is bad goalkeeping," Scholes told BT Sport post-match . "He could come out but he’s indecisive and I think that is their big weakness.
"He struggled for five years at Arsenal and it doesn’t look like he has improved for me."
Hargreaves, who also played for the Old Trafford outfit between 2007 and 2011, agreed with his colleague's comments and went one step further by suggesting that the Serie A giants will fail to win the competition with Szczesny between the sticks.
"Scholesy makes a great point about the goalkeeper," he stated. "How many sides have won the Champions League without a world-class goalkeeper?
"This team is ready to win the Champions League and people behind the scenes will be thinking have they missed a trick now Buffon has left."
Despite suffering their first defeat of the season in all competitions, Juventus remain top of Group H after four matches on nine points, two ahead of United in second.