The Nigerian has revealed that he told the former Blues winger that Petr Cech knew which way he would go, with the Czech goalkeeper indeed guessing correctly and keeping the effort out.
Roberto Di Matteo's side eventually prevailed 4-3 in a dramatic penalty shoot-out, in which Robben did not participate.
|WE ALWAYS BELIEVED - MATA
|Chelsea star says that his team were lucky but that destiny was on their side
"I just told Robben that he is going to miss it. You know, we just do that sometimes as players.
"I think when the penalty was missed, we kind of believed that this trophy was going to be ours."
The win ended billionaire owner Roman Abramovich's nine-year wait for Europe's top prize, in a season that had looked bleak following the departure of former boss Andre Villas-Boas in early March.
"I think we have made names for ourselves - we are the first club to win this trophy from London," Mikel added.
"We have shown what we can do. And, hopefully, people can stop writing us off."
The midfielder also hailed interim manager Di Matteo, praising the Italian for putting faith in him when he first took over from Villas-Boas.
Mikel continued: "When he took over, he had a word with me and said he knows how good I am, I am just maybe lacking a bit of confidence. And he gave it back to me.
"I would like to see him get the job, but at the end of the day, the club will make the right decision."