Gloucester maintained top spot in the Guinness Premiership with a 30-17 victory at Welford Road on Saturday to extend their winning start to the season and end Leicester’s unbeaten run.
Acting head coach Cockerill said: “We pride ourselves on our home record but we were not good enough and made some basic errors.
“We started reasonably well but the interception try put us in trouble. The penalty try seemed harsh - Julian White said he slipped. That left us on the back foot against a very good team and chasing the game.
“They were the better team, they had that little bit more nous. I am disappointed, but we take it on the chin and look at the positives as well as the negatives. We are four games into a long season and we have three wins on the board.”
Among the positives were the second-half tries from replacement Tom Croft and centre Matt Cornwell after Tigers had trailed 23-3 entering the last 20 minutes.
“I am pleased that we stuck at it and we scored two good tries,” Cockerill said.
“Gloucester played well, we did not play as well as we would have liked. We could have capitulated but the guys kept on going.
“It is easy to take the plaudits when we win, now we have to take the criticism when we lose. This was a lesson in lots of areas and we will deal with that. Now we need to concentrate on Saracens. Every week is a tough week in this competition and we will crack on.
“We have to deal with defeat, we are not used to it, but we will deal with it and learn from it.”