Gareth Bale walked away from a post-match interview when asked about his future after Wales were knocked out of Euro 2020 following a 4-0 defeat by Denmark in Amsterdam.
Kasper Dolberg struck twice before late goals from Joakim Maehle and Martin Braithwaite capped an excellent display by the Danes at the Johan Cruyff Arena.
Bale led Wales on the occasion of his 96th cap but, in the build-up to the tournament, there has been speculation that the 31-year-old may be contemplating retirement.
Asked if this would be his last game for Wales, Bale rolled his eyes and walked out of the post-match pitch-side interview.
Wales boss Page defended Bale's reaction to being questioned over his future by saying emotions were raw.
Page said: "He is feeling like any other player in the changing room. Disappointed.
"Why would he want to answer a question about his future? It's an insensitive question. What's the point of asking that?
"He's just come off the pitch after a defeat and emotions are raw.
"He's done the right thing by walking away and gathering his thoughts. It's about the group, what we do now moving forward and how we bounce back from that."
Wales started in promising fashion but never recovered from Dolberg's 27th-minute opener and lost their discipline in the closing stages.
Before he terminated his post-match interview, Bale told BBC One: "It was not how we wanted the game to go. We started very well for the first 25 minutes, but conceded a goal and the game changed a little bit.
"We came out second half trying to play and unfortunately made a mistake to concede the (second) goal which I guess killed the momentum on our side.
"Obviously to finish the game how we did is disappointing. The boys are frustrated and angry, it is understandable, and I would rather us go out like that, kicking and screaming than laying off and doing nothing."
Bale felt the second Denmark goal should not have stood for a foul on striker Kieffer Moore.
"I think the referee is being influenced by the crowd here, but it is what it is," the Real Madrid forward said. "There is no point in making excuses now, it is done. It is disappointing, that is all I can say."
Bale accepted Wales had "missed an opportunity" to reach the last eight.
"One thing we can't fault is the effort the boys have shown," he said. "That is the minimum requirement for this group and I am proud of them all still."
Wales' misery was compounded by the dismissal of substitute Harry Wilson for felling Maehle in the 90th minute.
Page echoed Bale's view over Denmark's controversial second goal and insisted it had a major impact on the contest.
"It sounds like sour grapes but it's a blatant foul on Kieffer," said Page.
"Sometimes you get the rub of the green, sometimes you don't.
"We didn't and within a few moments of a potential free-kick it falls to one of their players and we're 2-0 down.
"Then you've got a bigger mountain to climb."
Denmark boss Kasper Hjulmand said their tournament changed from the moment Christian Eriksen suffered a cardiac arrest in the opening game against Finland.
The Danes have since ridden a wave of emotion to reach the quarter-finals, where they will play either Holland or the Czech Republic in Baku.
"We were optimistic and believed in each other and the team before the tournament," Hjulmand said.
"Johan Cruyff is one of my greatest inspirations and we also know this is Christian's first home after leaving Denmark.
"This is where he played his first game at 15 years old and he is with us. I would love for him to have been here.
"It's hard to believe this is reality, but the guys are true warriors and being in a quarter-final is amazing."
