Ben Youngs, in his first start of the season, scored the only try and George Ford kicked the rest of the points as Tigers came from 8-6 down at half-time to secure the win.
Director of rugby Cockerill said: “They put us under a lot of pressure at times, especially in the first half. We thought it was a pretty soft try to concede but we had hardly any ball in the first half.
“They were very good for their lead at half-time but we kept our composure and talked about doing playing in the right areas of the pitch.
“They were desperate for that first win and they played well but our commitment in defence was as good as we’ve had in a long time and the discipline was very good.”
Tigers have taken 20 points from the opening six games, with four wins, one draw and only one defeat as the team head into the opening two rounds of the Heineken Cup.
“Those four points are very important in the context of the season as a whole,” said Cockerill. “It was a good win and a good way to go into Europe. Now we have to regroup and focus on Toulouse next Sunday.”