Kasper Dolberg scored a double as Denmark swept aside Wales, who had reached the semi-finals at the previous European Championships.
Welsh star Bale was asked if that was his last game for the national team after the game and walked away from an interview.
The 31-year-old Real Madrid winger had an underwhelming Euros campaign and has had plenty of speculation whirling around his future for both club and country.
“He is feeling like any other player in the changing room. Disappointed,” Page said.
“Why would he want to answer a question about his future? For me it’s an insensitive question. He’s just come off the pitch after a defeat.
“Emotions are raw. It’s about the group and how we bounce back from it.”
Page added he felt it was a cruel way for Wales to bow out of the Euros.
“Tough one to take. I don’t think the players deserved to leave the competition with that and how it ended up,” he said.
“I think for the first 25 minutes we were the better team. Their first shot on target was in the back of the net.
“They had to change shape after 25 minutes because they couldn’t cope with the three in the middle of the park, so credit to the players for doing that.”