Former Reds striker Suarez opened the scoring at Camp Nou in the semi-final first leg, with Messi capping an inspirational display with two goals in the final 15 minutes to seemingly wrap up the tie.
The Reds produced an amazing turnaround in the return fixture at Anfield, though, with Divock Origi’s early opener and two goals from Georginio Wijnaldum levelling the tie. Then, with 11 minutes remaining, Trent Alexander-Arnold's clever corner was turned in by Origi to secure an incredible 4-0 win and go through 4-3 on aggregate.
Liverpool went on to claim Champions League glory by beating Tottenham 2-0 in the final, which contributed to Klopp this week pipping Pep Guardiola and Mauricio Pochettino to win The Best FIFA Men's Coach award in Milan on Monday.
Asked about his favourite moment of 2019, Klopp told FIFA's official website: "The victory against Barcelona. It was the outstanding moment for sure. A lot of experts, myself probably included, wouldn't have bet money on us.
"Because being 3-0 down against a team with Messi, Suarez and all those players looks like a death sentence. We didn't believe we'd win, we just knew we had a chance, and we believed in that chance.
"It was massive. The support we had in the stadium. Looking back, we could say we won the Champions League in that game. All of us will remember it forever."
Klopp explained how he tried to inspire his side to one of European football's great comebacks.
He added: "I said [to the team], 'I normally wouldn't think it's possible, but because it's you, we have a chance'.
"That was exactly what I thought and what I felt. And from the first minute we were literally all over Barcelona.
"And at that moment, I thought 'we are ready at least', and it's very difficult to cope with a team like us and the atmosphere in the stadium in moments like this."