“It was a bit scrappy and we gave away a couple of soft tries, but Bristol fought very hard and made it difficult,” said acting head coach Cockerill after seeing the team come from behind to win 23-17 at the Memorial Ground.
Dan Cole scored a first-half try for Tigers but they trailed 14-7 at half-time after losing Matt Smith, Julien Dupuy and Marco Wentzel to injury in the opening period.
But the hosts were restricted to a single penalty in the second half as Dan Hipkiss latched on to a break by Ben Youngs to score a vital try for Tigers and Sam Vesty kicked 11 points.
“We put ourselves under pressure with a few mistakes and we had a bit of a wobble with the first-half injuries and then conceding a try before half-time,” added Cockerill.
“The tide turned a bit, but we regrouped, we kept the ball in hand better and in the end our discipline and shape saw us through.
“We dug ourselves out pretty well. The senior players - guys like Aaron Mauger, Ben Kay, Louis Deacon - took the game by the scruff of the neck and we did enough to win against a dogged and determined side.
“Wins like this in difficult circumstances show that we are making strides. I know from experience that this is not an easy place to come and win.”
Victory took Tigers to the top of the table for 24 hours, until Gloucester secured a 24-22 win over London Wasps on Sunday.
But defeats for Bath, Sale and Harlequins meant Tigers slipped just one place by the end of the Round 17 action.
“I am not worried about the table at the moment,” added Cockerill. “I am more worried about taking the points. If we keep winning we will be there or thereabouts.”
