Crsytal Palace manager Patrick Vieira was involved in an altercation with a fan following a pitch invasion at Goodison Park as Everton beat relegation.
The Toffees fought back from 2-0 down to beat Crystal Palace 3-2 and secure Premier League status in dramatic fashion.
As fans rushed onto the pitch to celebrate after the full-time whistle, cameras caught a fan taunting Vieira.
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The former Arsenal and France midfielder then appeared to kick out at the fan before he was ushered away by other supporters.
"I have nothing to say about that," Vieira said when asked about the incident.
Everton manager Frank Lampard added: "I feel for Patrick. I didn't get him at the end. I would have said, 'come in with us' - although he might not have wanted that.
"Of course he ran 80 yards across the pitch and it's not easy."
Lampard has come under fire this season as Everton were threatened with relegation from the Premier League for the first time in their history.
And they looked certain to be dragged into a final-day fight at the bottom of the table until three second-half goals saved the day.
Asked about the pitch invasion, Lampard said: "It was pure elation of fans who have come on the pitch after avoiding relegation.
"If it is done in the right way let them stay on the pitch, let them have their moment. As long as they behave, no problem."
The incident with Vieira came on the same night that Swindon players were involved in a confrontation with Port Vale fans following the second leg of their League Two semi-final play-off clash.
A fan was also jailed for 24 weeks for running on to the pitch and headbutting Sheffield United's Billy Sharp after the Blades' Championship play-off semi-final loss to Nottingham Forest on Tuesday.
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