Cole, who scored one of his side's penalties in the shoot-out, admits Chelsea rode their luck in the final as Bayern Munich spurned a number of good chances but felt they were deserving winners in the end.
He said on Sky Sports 1: "I'm lost for words. We should have probably lost the game with the amount of chances they had.
"We rode our luck, you need luck in this competition if you're going to win it. Today we rode our luck but we deserved it today."
Asked if he thought their luck might have run out when Bayern won a penalty five minutes into extra-time, the England international added: "Not really, with the players we've got here we thought, 'ok it's a penalty but we still have time had time left', and when Petr's making great saves like that we always believe."
The 31-year-old said: "This is the reason I came here."