The 33-year-old suffered the injury moments before kick-off and was assessed by a physio on the touchline. He chose to play despite the pain, completing all 90 minutes as goals from Youri Tielemans, Emí Buendía and Morgan Rogers sealed a dominant victory against the Bundesliga side.
Martínez was not asked to make any difficult saves in a match Villa controlled from the moment Tielemans converted a set piece in the 18th minute. He did however make two routine stops to preserve the clean sheet, doing so with a finger that buckled with each contact.
He was candid about the experience after the final whistle.
"Today I broke my finger during the warm-up and for me, every bad thing brings something good. I've done this my whole life and I'll keep doing it. Should I be worried? Well, I've never had a broken finger before.
"Every time I caught the ball, it went the other way. But these are things you have to go through, and I'm proud to defend Aston Villa."
The injury did not prevent him from joining the post-match celebrations in full. Martínez launched himself into the Villa supporters' section behind his goal before hoisting head coach Unai Emery aloft on the pitch in Istanbul.
The trophy is Villa's first major silverware since the League Cup in 1996 and their most prestigious since winning the European Cup itself in 1982. It ends a 44-year wait for European success and validates a four-year rebuild under Emery that has taken the club from mid-table mediocrity to continental winners.