The fan's efforts were foiled and he was pinned to the ground by keeper Marko Dmitrovic until police arrived to take him away.
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The scenes marred the end of a fantastic round of 32 clash between the two teams.
The Spanish side took a 3-0 lead going into the game and looked all set to be heading to the next stage of the competition.
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They were still sitting pretty with 13 minutes to go, before Luuk de Jong scored in the 77th minute.
Things then got interesting when Fabio Silva pulled another one back for the Dutch side deep into added time, needing one more to take things to extra-time.
PSV did not have enough time to that all important third goal, with Sevilla booking their place in the last-16.
Liverpool forward Cody Gakpo also made an appearance at the game as he said farewell to the PSV fans following his January move, just two days after his side were mauled 5-2 by Real Madrid at Anfield.
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