Suarez scored as Barcelona beat Juventus 3-1 in Berlin to win Europe’s elite competition and complete a stunning cup treble.
The Uruguay international joined the Spanish giants from Liverpool last summer and has tasted instant success – something Carragher says echoes his talent.
“In his last year at Liverpool, there was the talk saying ‘if we get top four, Luis will stay, he wants Champions League football’,” he said.
“I never believed that.
“Luis Suarez shouldn’t be playing Champions League football, he should be doing what he did tonight – winning the Champions League.
“That’s his ability – not playing in the competition, but winning the competition. I’m delighted for him.”
Suarez has enjoyed a prolific first season with Barcelona, scoring 25 goals in 43 appearances in all competitions.
Carragher, who played alongside Suarez at Anfield, admits he was concerned the forward wouldn’t be used to his full potential.
“There’s no doubt he was the best player in the Premier League by a mile last year,” he added. “Almost took Liverpool to the title, almost single-handedly.
“The one worry I had for him coming to Barcelona was ‘is he going to find himself in a wide position where he’s less effective’. Messi had that false nine role that we’ve talked about under Pep Guardiola.
“And you think, ‘will Messi ever be moved from there’. He’s almost, at times, bigger than the club – it’s a problem for the manager in how do you move him.
“But they got through that, and Suarez then became the focal point. Since Christmas, since they had the break in Spain, he’s been as devastating as Messi.”