Gayle, finally getting a run in the Eagles side thanks to injuries to fellow strikers Connor Wickham and Marouane Chamakh, was sent off a minute before half-time against West Ham.
Having already been booked for a needless lunge on Dimitri Payet, the 24-year-old then chopped down Cheikhou Kouyate to earn a second yellow card.
It left Palace having to play the entire second half with 10 men and, although they looked like holding out for a point, two late goals from Manuel Lanzini and Payet gave the Hammers a 3-1 win.
Gayle will now miss next Saturday's trip to Leicester through suspension, but defender Dann said: "He will learn.
"He was trying to do his best for the team and unfortunately he has ended up getting sent off and we have lost the game.
"When you look at it again you think he does not need to make that challenge, but these things happen
He wants to do well.
"He has got a run in the team after not playing much this season and he wants to impress
It was a bit too much enthusiasm I would probably say.
"It looked like one that he could have got away with, but when you are on a yellow card you always run the risk.
"It is difficult against teams like West Ham with 11 men, never mind 10
We were disappointed with the result."
Source : PA
Source: PA