Belgium, the world's second-ranked team, took a 13th-minute lead through Radja Nainggolan, but goals from Ashley Williams, Hal Robson-Kanu and substitute Sam Vokes sent Wales into a quarterfinal meeting with Portugal on Wednesday.
"It's a terrible disappointment. We're all gutted. We believed in our chances, but we're going home," said the 27-year-old Zenit Saint Petersburg player.
"We were doing well in the match until the 25th minute. Then there was a goal from a set-piece (by Williams, in the 31st minute). After that we conceded goals we could have avoided."
Belgium were without left-back Jan Vertonghen and centre-back Thomas Vermaelen due to injury and suspension respectively and their absence was felt at Stade Pierre-Mauroy.
"They're important players. We had to do without them," said Witsel.
"We never said we'd get to the final. But we wanted to give everything to achieve it."
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