The East Midlands club are now just outside the Aviva Premiership playoff places, despite pulling back a 17-6 deficit to draw level with a quarter of the game to go at the AJ Bell Stadium on Sunday.
However, Cockerill has suggested that Leicester have missed an crucial opportunity to make ground on their league rivals.
He told the club's official website: "There are five or six key moments in the match and you have to get them right. If you get four or five of them wrong then it costs you.
"We have only ourselves to blame on that. Today was an opportunity to put a gap between us and those teams around us and we have not taken it. We take the point and we're still well in the mix for the top four."
Leicester are now fifth in the standings.