The Athletic Bilbao player, a major transfer target for top European clubs, has been one of the most exciting players in Spain's seven-match winning run at the tournament.
He scored the opening goal in the 47th minute from a Lamine Yamal assist after terrorising England defenders on both wings.
"I will never forget this throughout my career. Every footballer dreams of this," Williams told reporters.
"At the end it is flattering for me. I always try to do my best in order to help my team. It is true that people are getting to know me and respect me and I appreciate that respect very much."
Yamal, the record-breaking 17-year-old who became the youngest scorer of the tournament's history when he netted in the semi-final win over France, had been hogging the spotlight but on Sunday he had little opportunity to shine.
Shut out throughout the first half, he found no space to start his runs. Instead, it was left to fellow winger Williams to charge down the wing.
Williams even had to support Yamal on the right wing for long periods as Spain struggled to break past a disciplined England backline.
Williams repeatedly broke past England's Kyle Walker down the left but his deliveries into the box failed to find a Spanish teammate.
Two minutes after the restart, however, he did not need anyone's help when he picked up a pass from Yamal and fired a superb low shot past England keeper Jordan Pickford.
"It has been an incredible year for me," said Williams, who was born in Spain to Ghanaian parents and whose brother Inaki plays for the Ghana national team.
"My parents have suffered a lot to get here ... they have instilled respect and loyalty in me."
Williams kept going after England levelled through substitute Cole Palmer in the 73rd minute, pushing Spain forward to secure their fourth European crown courtesy of substitute Mikel Oyarzabal's late winner.
