The Reds went into the game having beaten Red Star 4-0 at Anfield a fortnight ago and knew that another victory would see them take charge of Group C.
But a first-half double from forward Milan Pavkov was enough to see off Jurgen Klopp’s side on the night, with Liverpool’s chances of qualifying for the knockout stages now in doubt.
And Degenek, who was excellent at the heart of the Red Star defence, believes Liverpool were too complacent.
“We played well and managed to shut them out. Pavkov scored two beautiful goals, but all the boys played really well. Now if only we could play like this every week," Degenek said, as per the Liverpool Echo.
“I think Liverpool underestimated us and consequently paid for that mistake.”
Klopp’s side had been warned to expect a hostile atmosphere at the Marakana on what was a hugely significant night for Red Star, who are back in the Champions League this season after a 26-year absence.
The victory was their first in Group C and means that there are now just two points separating first and last spot.
Degenek went onto claim that James Milner, who was Liverpool captain on the night, had told him that the rowdy crowd in the stadium was like nothing he’d ever heard before.
“I spoke with Milner in the tunnel and he told me he'd never experienced anything like the noise coming from above,” the Australian defender added.
“I believe we can repeat this against Napoli.”
Unsurprisingly, Red Star goalscorer Pavkov was delighted with his efforts on the night after not featuring in the first match between the two sides at Anfield last month.
“I was hoping for this,” the striker said.
“I said earlier that I'd like to score against Liverpool and it came true. I even scored twice.
“Sleep? I won't. I can't sleep after some league games, let alone this one. Maybe not the next two or three nights.”
Liverpool are set to take on PSG at the Parc des Princes in their next group match before they host Napoli in December.