Wales boss Gary Speed has offered his condolences after a fan died following a suspected assault before the clash with England on Tuesday night.
Wales supporter Mike Dye, 44, of Cardiff, suffered a heart attack at Wembley before he was rushed to hospital with head injuries.
Six men - all believed to be Wales supporters - are being questioned by police about the incident.
Speed says the Wales team did not know about the incident until after their 1-0 defeat to England in the Euro 2012 qualifier.
He told Sky Sports News: "The players and the staff, we're all deeply saddened by the news that we found out after the game and our condolences go out to the families involved.
"I know there's a police investigation going on so that's all we can really say on the matter."
He agreed the event had overshadowed what had been a good performance by Wales at Wembley.
"Yes absolutely. I mean it's a game of football at the end of the day and there's nothing more precious than life and like I say, our condolences go out to the man's family."
Mr Dye was found with head injuries on a concourse area outside the turnstiles at the venue at around 7.20pm on Tuesday night.
Paramedics revealed he had also suffered a heart attack before being rushed to a North London hospital.
Colleagues at Cardiff Council, where Mr Dye worked in the highways department, have been left devastated by his death.
Council chief executive Jon House said: "Staff at the authority are devastated at the loss of their colleague and friend who gave almost 20 years of good service to the council in a very specialised service.
"Our thoughts are with his family at this tragic time and we will be offering support to his family and work colleagues."
Thousands of people have left messages on a Facebook tribute page entitled RIP Mike Dye.
Several refer to his wife, Nathalie, and children in brief messages of tribute.
Lisa Kavanagh wrote: "to mikey a really nice person who has been taken away to (sic) soon god bless to you rip mikey and to all ur family my deepest sympathy to you all god bless lisa k and family xxxxxx."
Carol Binding wrote: "R.I.P. Mike...I did't know you...but like so many others, I am sickened to hear about this ...my thoughts and prayers are with your family and friends at this sad time. Sleep Tight and God bless."