“It’s a great start for me personally to get my confidence up and to help the lads get the win is the most important thing,” Bellingham said.
Harry Kane so nearly extended the lead in the second half when Serbia goalkeeper Predrag Rajkovic pushed his far post header onto the underside of the bar.
Kane set a record for his country by making his 23rd appearance at a major tournament.
“It’s a tough game. They are a tough team and have good players,” the England captain said. “We stood up to it well and it is good to get the three points and (for us) to progress. It’s good that we got the win today.”
Victory sent England to the top of Group C after Denmark drew 1-1 with Slovenia in an earlier game, with Christian Eriksen scoring three years after suffering a cardiac arrest on the field at the last Euros. England plays Denmark in Frankfurt on Friday.
England was a beaten finalist at the last Euros, losing on penalties to Italy in the final three years ago. It is one of the favorites this time around. Serbia is playing in the Euros for the first time since 2000.