The USA's World Cup campaign came to an end at the last-16 stage after they were beaten 2-1 by Belgium in extra-time at the Itaipava Arena Fonte Nova on Tuesday.
Klinsmann's men gained plenty of admirers for their performances in Brazil but Donovan - the USA's all-time leading scorer - was less than impressed by the tactics adopted by the German coach, who controversially overlooked the 32-year-old LA Galaxy forward for the World Cup.
"It's certainly a missed opportunity," Donovan, who has scored 57 goals in 156 international appearances, told reporters on Wednesday.
"The thought of having a game Saturday – the day after the Fourth of July, against [Lionel] Messi and Argentina, with what was already a swelling audience – would have been incredible.
"I think we're all disappointed in what happened yesterday. I think the most disappointing is we didn't seem like we gave it a real effort, from a tactical standpoint.
"I thought the guys did everything they could, they did everything that was asked of them, but I don't think we were set up to succeed yesterday, and that was tough to watch."
Donovan added: "It's a results-oriented business, and so, results-wise, you can hold your head high.
"But If you really look at the performances, there were some good performances by guys, some not-so-good performances by guys. As a whole, I think tactically, the team was not set up to succeed.
"They were set up in a way that was opposite from what they've been the past couple years, which is opening up, passing, attacking – trying to do that. And the team's been successful that way.
"Why they decided to switch that in the World Cup, none of us will know. From a playing standpoint, I think the guys will probably be disappointed in the way things went."
Donovan - a veteran of three World Cups after appearances in 2002, 2006 and 2010 - said he would have questioned Klinsmann over the team's formation had he been in South America.
"If I'm in that locker room before that game – before the Germany game, before the Belgium game – and the coach walked in and said we're playing a 4-5-1 and Clint [Dempsey] is up top by himself, I would have been disappointed.
"Because I would have said 'let's go for it. I want a chance to go for it and try to win the game'."
