Marie-Antoinette Katoto and Sandy Baltimore struck in the first half for France to leave England's travelling fans in stunned silence and while Keira Walsh pulled one back in the 87th minute and the Lionesses had some near-misses towards the close, it was too little too late for the reigning champions.
"I'm disappointed there was some cheap sort of emotional defending in the first half, when you take waves of attack like that you leave yourself open to those sorts of things," Williamson said of their poor one-on-one defending.
"I'm just frustrated because I think the football that we played near the end, and the game plan, could've worked. We just didn't execute it exceptionally well.
"We spoke (at halftime) as players, we take responsibility individually and as a team. We have a calm environment at the minute but there was an injection of get the emotion out, leave it in the changing room, and go out and just be pragmatic about it and try and insert a bit of 'umph' into the game."
The loss was manager Sarina Wiegman's first in a European Championship after leading both the Netherlands (2017) and England (2022) to titles.
"Of course we're frustrated, we had three very good weeks and we trained really well but that's never a guarantee that you'll win the game," Wiegman said. "And you also know that France is a proper team too, so you have to do things really well. We just didn't get it right at those moments."
The first goal of the night almost went to England but Alessia Russo's strike was chalked off after VAR ruled that Beth Mead had been offside in the buildup.
Wiegman also believed Russo was fouled on France's second goal but a VAR review said otherwise.
"I'm not the referee but I'm upset," she said.
England have been slow off the start in previous major tournaments, edging Austria 1-0 to kick off Euro 2022 and Haiti 1-0 at the 2023 World Cup en route to their first final appearance.
"I can't really compare all the first games in tournaments," Wiegman said. "I think playing against France is just totally different than every other start of a tournament because I think they're a world-class team, and I think we're a very good team too."
England now face a mammoth task on Wednesday against the Netherlands, 3-0 winners over Wales in Saturday's other Group D game.