The four national football associations were unable to agree on sending Great Britain teams to Rio.
Sampson, who led England to a bronze medal at the 2015 World Cup, described the situation as "frustrating".
"I've watched the tournament and I believe this team would have won the gold medal," he said.
"This group of players did earn the right to go to an Olympics and represent themselves and their country, but it's been taken away from them".
England captain Steph Houghton, who scored three goals at London 2012 for Great Britain, added that it was "very disappointing" to not go to Rio.
"That was originally our place - the place that we won at the World Cup, and it's hard, but at the same time there's no point about complaining we can't be there," she added.
England's Football Association had put forward the idea of sending Great Britain teams to the Olympics, but Fifa said it would need the agreement of the ruling bodies in Scotland, Wales and Northern Ireland, who were against it.
Stewart Regan, the Scottish Football Association's chief executive, has been among those to voice concerns that a Great Britain team would threaten the separate status of the home nations at future international tournaments such as World Cups.

The work, entitled Duality, is formed of diptychs, with each person posed in their own clothing and their workwear. The aim is to see how a viewer responds to the uniform and how it shapes their perception of that person - how we prejudge based on a uniform or a certain look and style.
Of course, what we wear also affects us, our approach and how we feel.
What is your response to these pictures?
The images are on show at the No Walls Gallery as part of the Brighton Photo Fringe Festival. I'll be highlighting some other work on show at the festival next week.
All photographs courtesy Strand Collective.
Great Britain could have won another Olympic gold had the women's football team been allowed to compete, believes England head coach Mark Sampson.
[NEXT_CONCEPT]
New work by Simon Bray and Tristan Poyser explores the way in which our clothes shape us, that outer shell we use to accentuate or sometimes hide who we are.