Williamson urges fans to remember England have enjoyed an incredible run of results
The men were defeated 2-1 by Spain in Sunday's European Championship final, which follows their loss to Italy on penalties in the final of the last edition of the tournament three years ago.
On Tuesday, England, the holders of the women's Euros title, face Sweden away. Victory will secure England a berth at Euro 2025.
"Yeah, devastated for (the men), especially knowing some of them personally as well," Williamson told reporters.
"What (men's manager) Gareth (Southgate) and his team have done over the last three, four years, reaching (two successive Euro) finals and bringing that dream closer to reality, we are very lucky as fans of England, men's and women's, to be in the position that we're in.
"They didn't quite get over the line to a fantastic Spanish team, I know they'll be devastated about it, it will take a while for them to get over it.
"But us as a country, we've been blessed with incredible tournaments. And when those wins come, which I do believe they will, then they'll be even sweeter."
The women, who beat Germany to win the Euro 2022 and then finished runners-up to Spain at last year's World Cup, are within touching distance of a Euro berth after their 2-1 win over Ireland on Friday.
The Lionesses are second in Group A3 on 10 points, two behind France, who clinched their berth with a 2-1 win over Sweden.
England need only a draw with the Swedes, who have seven points, to go through.
The top two teams in each of the four groups in League A will join hosts Switzerland in the finals, while the remaining pairs go into a series of playoffs for the seven remaining spots.
Williamson captained England to their European triumph two years ago but missed the World Cup after suffering a torn ACL. She returned to the England squad in late March ahead of their Euro qualifiers and is thrilled to be back.
"I love playing for England, I think anyone that gets to wear this kit is very lucky and we know it," the Arsenal defender said. "It's been an exciting time.
"It's a pressurised situation. It's competitive football. We're trying to qualify for a tournament which is sort of the last great memory that I have in football, so I've been very motivated and I've loved being back in the fold.
"But you chase a certain level of consistency with your own performance, which is a journey in itself."
England women's manager Sarina Wiegman knows the heartache of coming close to victory after their World Cup final loss to Spain and was asked what the next few days and weeks might be like for Southgate, who said he has not yet decided on his future with the team.
"Takes about three weeks, it took me three weeks to get over it," she said matter-of-factly.
"It's very hard ... when you have given your everything, then you hope you win and when you don't, you are really disappointed.
"But then you start thinking: Okay, did we get everything out of ourselves? Did we do everything that we could that was in our control?
"And then you have to accept it. It's easier to accept a win than to accept a loss but yeah, for me that takes it took a while."