Tigers stayed top of the table on 49 points from 16 games despite a 19-3 defeat at Franklin’s Gardens. Saints are one point behind with a game hand, Saracens remain third after a 14-16 home defeat by Bath on Sunday, and London Irish complete the top four – and head for Welford Road next weekend.
“We just weren’t good enough,” said Cockerill soon after the final whistle on Saturday.
“We’ll have a look on Monday, we’ll deal with it in training and we need to react in our next game.
“We had lots of possession and little to show for it. Saints defended well and it is frustrating that we gave away some really poor penalties and we paid the price. We have the best discipline in the league according to the stats so that is disappointing.
“If you give a side a toe-hold in a game like that it is hard to come back.
“Everybody takes responsibility for it, starting with me, and we will have a good look at what we did and didn’t do. Defeat does not taste very nice at the moment but we have to accept it and make sure we are stronger and better next week.”
London Irish arrive at Welford Road on Saturday (5.35pm) in the last league game played during the Six Nations window.
“We’ve won two from three now in this period,” added Cockerill. “It is a difficult time with players coming in and out but we have to deal with it and get on with it. We have a squad that is good enough to do that.”
Back-rower Craig Newby led out Tigers for the first time as captain, and could not disguise his disappointment at the final whistle.
“We played some really good rugby in the first 20 minutes but we were a bit indisciplined,” he said.
“They are a good side, they kicked their penalties and they took probably the one real scoring chance in the game.”
Asked for any positives to take out of the game, Newby replied: “It was good to get Julian White back and see him play the full 80 minutes.
“I think we did put some good phases of play together at times, but there were a lot of little mistakes.”
Tickets for Saturday’s match at Welford Road are on sale now from the Tigers ticket office. Phone the hotline on 0844 856 1880, book online or call in now to guarantee the best available seats.