Dutch goalkeeper Daphne van Domselaar was named player of the match after keeping South Africa, and in particular striker Thembi Kgatlana, at bay with a series of fine saves.
"We felt we could have won this game and if I look back, we should have won with the opportunities that we had," Ellis told reporters.
"But, as always, if you don't take the chances then that's what happens.
"With a decision or a goal here or there, we could be speaking differently now, but I think the whole of South Africa should be really proud of this team."
Ellis hoped that people would remember all the saves that goalkeeper South Africa Kaylin Swart made at the tournament, and not just the howler that gifted the Dutch their second goal after halftime on Sunday.
Swart appeared to have the shot from Dutch forward Lineth Beerensteyn well-covered but did not get her body behind the ball, which came out of her hands and bounced into the net.
"There's nobody in the world who is perfect and you're going to make mistakes and unfortunately that happened, but she kept us in it as well," Ellis said.
"I hope will people remember her for how she played, and not that one incident."
Ellis said that overall a first trip to the last 16 made it a successful tournament for South Africa, even if she was left wondering what might have been had they taken their chances in front of goal on Sunday.
"I think I'm more disappointed than anything," Ellis concluded.
"I think as a group, we need to hold our heads up high. When we qualified for the last 16, the whole country went crazy and I'm expecting them to go crazy when we get back.
"This team really punched above their weight considering that we do not have what everybody else has - a professional league."
