Wales marked their first appearance in a major tournament since 1958 with a 2-1 victory in Bordeaux, Gareth Bale and substitute Hal Robson-Kanu the scorers.
Northern Ireland play their first Group C game on Sunday against Poland in Nice (17:00 BST).
In Marseille, Tottenham's Eric Dier put England ahead in the second half but they were denied victory by a stoppage-time equaliser from Vasili Berezutski.
England boss Roy Hodgson told BBC Radio 5 live: "When you concede with one minute left, it is a bitter disappointment.
"In the first half I thought that was as good a performance as we are capable of giving.
"It feels like defeat because we were preparing to celebrate a victory and we don't have that possibility now."
The end of the game was overshadowed by more clashes between rival fans.
Russia supporters appeared to rush at the England contingent, and BBC Radio 5 live's Mark Chapman said: "The mood in the stadium had been fine until about five minutes to go - at which point two flares were set alight in the Russian end.
"It then looked like a firework was launched from that end into the night sky and the mood in the stadium then notably changed."
The latest violence followed two nights of trouble in the French port city, where tear gas and a water cannon have been used by police.