Former Wales striker Bellamy, who was appointed national boss in July 2024, faced criticism from some fans after holding talks over a potential move to Burnley in June.
In a lengthy news conference after the Norway triumph, he said he feels people “could be kinder to each other” after revealing the negativity aimed at him had also affected his family.
“It’s not me but I have kids and a wife; it’s for them – they see it,” he said.
“I’ve lived in this environment and I had it as a player, but I think there’s ways we can speak to people, and just because it’s the game we love, it doesn’t give us the right to think we can say whatever we want to.
“We’re such a small country, I’m like… why can’t we have each other’s backs? Why don’t we look after each other more? Maybe that’s me.
“I’m not saying everyone’s above criticism, far from it. But I think it’s too easy, and we’re too quick.”