He revealed his overarching message to the players was that they could not afford to pass up any more scoring opportunities once competitive football returns against Southampton next week.
"We’ve got to start taking chances," Hodgson said. "I’ve just told the players that. They know it, of course; I’m preaching to the converted but you can’t feel that satisfied with the game standing here and it’s 1-1 when you know it should have been a victory by at least two or three goals for us.
"I find it hard to take at the moment. First Millwall, we should have put that to bed on at least two or three occasions, but today I think [we had] 20-odd really good opportunities and, quite frankly, five or six of them were such clear goal chances I can’t believe we didn’t put the ball in the back of the net.
"But I thought they [Brøndby] were good, I thought it was a really good test and I’m more than happy with the quality of our play. I thought at times the attacking play was of a really good class. We were making the opportunities, getting in behind the defenders and cutting their defence open."
Hodgson continued his praise of Palace's performance, saying: "There were some really good individual performances and they [Brøndby] are a good team. It’s certainly the strongest team we’ve played in pre-season, but I thought we defended well.
"The back four once again and goalkeeper were really good and I thought our attacking play produced the goal chances we were hoping it would produce."