Wales lost 2-0 in Aarhus after a Christian Eriksen brace, with the second goal coming from the penalty spot after Ethan Ampadu was adjudged to have handled in the area.
Stand-in captain Bale was particularly frustrated by the decision and suggested that the call would not have been made if Denmark were the away team.
"But for me, it wasn't a penalty. It was very soft.
"Maybe if it's not at home, it's not given. That made it a lot more difficult for us being 2-0 down. At 1-0, we were still in the game, still fighting hard."
Manager Giggs added: "In the second half, we started really well. We were in it and then the penalty decision. Whether it was a penalty, yes or no? I don't know. It's harsh.
"Then, after that, it's an uphill task against a good team."
Before and after the penalty, Wales fell below the standards set in a 4-1 thrashing of the Republic of Ireland on Thursday, but Giggs is determined to get his side performing on a consistent basis.
"It's about coming back. We set the standard on Thursday and to repeat that is difficult, but that's what I've challenged the players to do," he said. "I think that we can do it.
"Overall, I can't fault the effort. We had two games in a short space of time and we were in it up until the penalty decision."