Sweden progressed to their first ever Olympics semi-final 4-3 on penalties after a 1-1 draw in Brasilia as Sweden coach Pia Sundhage ousted the US team she led to gold in 2008 and 2012.
"We played a bunch of cowards," Solo told Sports Illustrated.
"The better team did not win today. I strongly believe that. I think you saw American heart. You saw us give everything we had today."
Star striker Alex Morgan and substitute Christen Press missed penalties before Lisa Dahlkvist converted the winning spot-kick despite Solo's best efforts to put her off by changing gloves to delay Dahlkvist's effort.
"It is ok to be coward if you win," Sundhage shot back.
"What she did was an act of panic," said Swedish 'keeper Hedvig Lindahl of Solo's time-wasting tactics before the final penalty.
USA coach Jill Ellis tried to diffuse the row.
"They executed her game plan very well. It's a matter of knowing how to use all the resources you have," said the Englishwoman.
"And finally the most important thing is the result, not how to play."
Sweden will now face either hosts Brazil, who thrashed them 5-1 in the group stages, or Australia in Tuesday's semi-final in Rio.
"I don't think they're going to make it far in the tournament. I think it was very cowardly," added Solo.
"But they won. They're moving on, and we're going home."
Defeat is the Americans' first in 15 games at the Olympics and only their third ever in Games history having won four golds and a silver since women's football was introduced to the Olympic programme.
Morgan looked to have saved America's blushes when she swooped 13 minutes from the end of normal time to cancel out Stina Blackstenius's opener just after the hour mark.
But the world's number one ranked side failed to break down Sundhage's well-organised Swedes in extra-time, who also had a perfectly good goal from Lotta Schelin wrongly ruled out for offside in the final minutes.
"They didn't try and press. They didn't want to open the game and they tried to counter with long balls," continued Solo.
"We had that style of play when Pia was our coach."
Sundhage insisted she had full faith the Swedes could pull off a massive upset despite scoring just twice in three matches as they sneaked into the last eight as one of the two best third-placed sides from the group stages.
"When I looked at my players before starting the extra time and penalties and I was so confident in my players," she added.
Solo's Games has been dogged by controversy as she received chants of "Zika" from fans across Brazil for Twitter posts on her elaborate precautions against the virus.
Canada maintained their perfect record in Brazil to set up a semi-final with Germany in Belo Horizonte thanks to Sophie Schmidt's winner in a 1-0 win over France.
Bronze medallists in 2012 when they lost a thrilling semi-final to the USA 4-3 in extra-time, Canada have another chance to reach the Olympic final for the first time as Schmidt volleyed home 11 minutes into the second-half from Janine Beckie's inch-perfect cross.
Germany overcame 10-man China in Salvador with Melanie Behringer netting the winner 14 minutes from time.
China had Wang Shanshan sent-off early in the second-half and also missed the chance to send the game into extra-time when Wang Shuang hit the post with a penalty six minutes from time.