5 February 2016 Last updated at 13:30 GMT
Mobile phone footage of the Toffees boss showing off a series of slick moves at the Jason Derulo gig has been shared thousands of times on Twitter.
Martinez later confirmed he was at the event and said he was a "big fan" of the American pop star.
And he said: "I have better moves, believe me. Probably that [seen on the video] was the worst move."

Shadow Scottish Secretary Margaret Curran has written to the UK government offering support for early legislation.
The Scottish government has already called for action before Westminster breaks for the general election.
Scottish Secretary Alistair Carmichael has said officials are looking at the options.
These are likely to include a section 30 order which is much less complicated than an act of parliament.
In a letter to the Scottish secretary, Ms Curran said: "I am writing to offer our support for a Section 30 order to devolve the franchise to the Scottish Parliament immediately if it is brought forward by the government.
"This will ensure that there is enough time for the Scottish Parliament to make the changes necessary to ensure 16 and 17-year-olds are able to vote in 2016."
The Smith Commission on further devolution called for the UK to "devolve the relevant powers in sufficient time" for that election.
Its recommendations were agreed by all five political parties in the Scottish Parliament.
The independence referendum was the first national vote in which 16 and 17-year-olds were able to take part.
The chief counting officer for the referendum, Mary Pitcaithly, chairs the board that oversees election management in Scotland.
She said: "If changes of this significance are going to be made, the earlier that election professionals know about this the better, so that appropriate preparations can be made to minimise any risks".
Mr Carmichael discussed the issue with Scotland's First Minister Nicola Sturgeon last week.
Ahead of that meeting he said he saw "no reason" why votes at 16 could not be in place for the 2016 vote.
Labour also wants him to consider which other powers might be suitable for fast-track devolution.
Ms Curran said: "Many of the Smith Commission proposals will require primary legislation, and Labour will introduce a Scotland Act in our first Queen's Speech.
"However, it is right that we should assess which powers could be passed more quickly and where the Labour Party could offer its support."
The Scottish government has specifically called for early control of air passenger duty and disability living allowance.
But the Scottish secretary has described votes at 16 as an "exception" to the general principle that further devolution "will proceed as a package".
Mr Carmichael was asked about when tax powers would be devolved at a Holyrood committee last week.
He said: "With the budgetary consequences that come with that, there is probably a greater interest in ensuring that you get the whole thing as a package rather than taking it in dribs and drabs."
Everton manager Roberto Martinez has been spotted dancing the night away at a concert in Manchester.
[NEXT_CONCEPT]
Labour wants the immediate transfer of election powers to Holyrood to allow MSPs to give 16 and 17-year-olds the vote in 2016.