However, Jurgen Klopp's men managed to defy the odds and progress to the last eight, securing a 3-1 win at the Allianz Stadium thanks to a Sadio Mane brace and a Virgil Van Dijk header.
With the quarter-final draw set to take place on Friday morning, Liverpool legend Carragher insists his old club can use their latest victory as a springboard to win the competition come May.
Speaking after the game Carragher stood alongside Van Dijk and spoke to Viasport Fotbal, praising the Dutchman for his role in the win over Bayern before revealing his bold prediction.
"Top performance tonight in a hostile atmosphere, certainly going 1-1 before half-time," the ex-England defender began.
"I thought the performance in the second half from the man himself [Van Dijk] but certainly from the whole team was one of the great Liverpool away performances really.
"I never felt Bayern Munich were going to score. I felt yourself [Van Dijk] but also Matip, he gets the own goal in the first half – it wasn’t a mistake it’s just one of those things – I thought he was outstanding as well at the back.
"And if you can keep that going through now… I fully believe Liverpool can go all the way in this competition."
Van Dijk then chipped in to discuss Liverpool's performance, highlighting his partnership with Joel Matip as a key factor in their latest triumph.
Bayern hitman Robert Lewandowski was tipped to cause the Reds plenty of problems at the Allianz, but he was ultimately unable to find a way past the intimidating centre-back duo.
"You need to give him so much respect, he’s a fantastic striker," Van Dijk said.
"Me and Joel did well, he didn’t score so its always a good thing but he's a fantastic striker and he's shown it down the years.
"It wasn’t about me and him but I think its always difficult to play against me and Joel together."
Klopp must now prepare his side for a trip to Fulham on Sunday, where another win could see Liverpool return to the top of the Premier League.