Um, maybe it practice. If it says, Practice, then you earn no Arena Tickets. If you enter the Pet Derby, you will get Arena Tickets. But, I never, ever did not get Arena Tickets from Pet Derby. But, if you did, then thats bug. Report it to KI.
Were you racing in Ranked derby or Practice derby? I'm sure you know the difference, however, i will tell you anyway. Ranked derby gives you points, while practice is just for fun and does not give you any points. You might have accidentally went on practice derby instead of ranked derby, so you are not clueless, lol. If your sure that you went on ranked derby, than this is probably a glitch and will most likely be fixed soon if anybody else is having this problem. Mary Ravengem, Balance, Death, Sun, Star, Moon, lvl 60