Everton found themselves two goals behind at half-time but were immense in the second period.
Michael Keane, Richarlison and Dominic Calvert-Lewin sent supporters into raptures and they stormed the pitch at the final whistle to celebrate the Blues retaining their top-flight status.
Video footage has emerged of Palace boss Vieira appearing to kick an Everton fan when making his way to the visiting dressing room on the other side of the ground - having been goaded beforehand.
More footage, which appears to be filmed by the fan himself, shows the fan gesturing in Vieira’s face and sticking the middle finger up at the Palace manager.
The supporter also shouts expletives at the former Arsenal midfielder before he appears to react.
Other Everton fans then intervene and help the opposition boss get back to the away dressing room.
When asked about the incident, Vieira responded: “I do not have anything to say about that.”
The incident comes just days after Robert Biggs was jailed for 10 weeks for headbutting Sheffield United striker Billy Sharp following their loss to Nottingham Forest on penalties at the City Ground in the Championship play-off semi-finals.
Lampard initially giggled when he was told about Vieira’s actions.
But swiftly turning serious, the Everton's boss said he believes pitch invasions are fully warranted given what was achieved - as long as they are conducted in the right manner.
Frank Lampard’s reaction to pitch invasion
Lampard said: “There were none (issues with players).
“I feel for Patrick because I didn’t get him at the end because of how it all erupted for us.
“I would have said: ‘Come in with us’ (into the Everton dressing-room area rather than the Crystal Palace area on the other side of the pitch).
“They might not have wanted that but I’d have said: ‘Come in with us’. I know how managers feel and I get that.
“And, of course, he’s running across the pitch of 80 yards of our fans coming on. It’s not easy.
“There’s nothing from me. Not any issues. it was pure elation of fans who want to stay in the Premier League that come on the pitch.
“I can’t complain when I’m on the directors’ box in front of them. It was a special moment for the football club.
“If done in the right way, let them stay on the pitch for a bit. As long as everyone is behaving and we don’t see scenes like the other night, everyone is behaving, happy and go home. That’s what football is all about.
“What are we going to do, handcuff them to the seats when we go 2-0 down and win 3-2 and stay in the league? As long as they behave, no problem.”