Quins claimed a vital breakthrough with a Nick Easter try on the stroke of half-time and celebrated a try from Matt Hopper five minutes into the second half as they gained reward for their advantage in territory and possession.
Tigers took only a point in a 23-16 defeat, but Cockerill insisted the late rally was no consolation for a poor team performance, especially in defence.
“Quins came, they played better than us, they deserved to win,” said a bitterly disappointed Cockerill.
“I’m not going to make excuses. They ran at us and we didn't tackle well enough. Every time they ran we conceded metre after metre and that is not good enough.
“We didn’t get off the line and make our tackles and we let them play. That is disappointing because we have been very good in defence this season.
“We’ve had a lot of injuries and lots of players unavailable to us, but I’m not going to accept that performance and neither are the players.
“Quins played well and deserved to win at Welford Road and that hurts.”
Tigers trailed 23-9 going into the final minute before the pack gained a penalty try at a close-range scrum and Owen Williams added the conversion for the losing bonus point.
“The point is no consolation,” insisted Cockerill. “I don’t think we should be pleased with ourselves for getting stuck in and being able to get a point in the end. Our expectations are higher than that and the players are better than that.
“I’m not accepting the performance, but I will take responsibility for that and for getting us back on track again. There are no short-cuts, we just have to work hard and get going again.
“We’ve got lots of players missing and lots of new combinations in the team but we have to be better than that.
“You see the true colours of people when things are not going well and that includes myself.”
Tigers are back on home soil on Friday evening in the opening LV= Cup tie of the season against the Ospreys. Kick-off is at 7.45pm and tickets are available now. Games in the pool stages of this competition are included in season tickets.