Ulster retained top spot in Pool 4 of the Heineken Cup with a four-try victory at Ravenhill, with skipper Geordan Murphy providing the only try for Tigers.
When Billy Twelvetrees converted the Murphy score, Tigers were back in the game at 10-7, but Ulster scored again just before half-time and pulled away after the restart.
“Sometimes you just have to take it, shake hands and say well done,” said Tigers director of rugby Cockerill.
“Hats off to Ulster for the way they played, they played well and we just never got on to the front foot enough.
“It is a hard place to come to play. We struggled to get a foothold in the game and we struggled for field position.
"They took their chances and built their score. They defended very well, attacked the breakdown and, tonight, we couldn’t cope with it. Ulster deserved their win and there was not a part of the game where we had dominance.
“Ulster came out of the blocks quickly but we got back into the game with a neat try. Unfortunately, we could never get hold of the ball for long enough to build pressure.
“With hindsight, this is our fourth game in 18 days and maybe that caught up with us. We had some key guys out but the side we had was good enough to put up a better show.”
The last game in Pool 4 sees Tigers host Aironi at Welford Road on Saturday. Kick-off is at 3.40pm and tickets are available now.