A low-quality match in Budapest went all the way to a penalty shootout, with Sevilla winning 4-1 after the two sides played out a 1-1 draw in 120 minutes of at times turgid football.
The result also means Tammy Abraham fail to become the first player to win the Europa Conference League, Europa League and Champions League.
Roma drew first blood through Paulo Dybala's composed finish in the first half but Gianluca Mancini's own goal saw the match go to extra time.
There were very few chances in the extra 30 minutes as the final drifted to a shootout.
It was Roma who blinked first as Mancini had his spot-kick saved while Roger Ibanez hit the post with his effort. Sevilla scored all their penalties with Gonzalo Montiel's strike securing the victory.
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The LaLiga side's perfect record in Europa League finals is extended to seven wins, while Mourinho has lost his first of six European finals.
The Portuguese immediately removed the runners-up medal from his neck after being presented with it by UEFA delegates.
Mourinho then handed the medal into the crowd, which was collected by a young fan, while Sevilla celebrated with the prize that both sets of players wanted.