Wales suffered their biggest ever defeat in the tournament and were knocked out at the Euro 2020 last-16 stage in Amsterdam.
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Bale has refused to comment on his club or international future during the competition and when a BBC reporter asked if he had just played his final game for Wales, he walked away from the interview.
The 31-year-old has made 96 international appearances and was the standout performer when Wales made the semifinals at Euro 2016.
After the game, Wales coach Rob Page defended Bale’s actions and told a news conference: “He’s disappointed, why would he want to answer a question about his future? He’s hurting.
“It’s an insensitive question — he’s done the right thing by walking away and gathering his thoughts. It’s about the group and what we do moving forward.”
Wales players were unhappy about Denmark’s second goal because they felt striker Kieffer Moore was fouled in the build up.
Before walking away, Bale was asked about the incident and replied: “If you play the ball through the back of someone it’s a foul.
“I felt the ref was influenced by the supporters here. It’s disappointing that’s all I can say.”
The Wales captain also added that he was disappointed with the result but pleased with the effort from the squad.
“It’s not how we wanted the game to go, from our point of view we started very well and then the game changed,” Bale said.
“We tried to play in the second half but made a mistake to concede which killed the momentum on our side.
“To finish how we did is disappointing but the boys are frustrated and angry understandably, I’d prefer us to go out that way.
“We’ve missed an opportunity but I can’t fault the effort and that’s the minimum requirement, I’m proud of them still.”