A try from Dan Bowden and 17 points from captain Toby Flood gave Tigers four vital points in the ninth round of Aviva Premiership action.
“Away from home you have got to get the points and we’ve done that,” Tigers director of rugby Cockerill said.
“The boys kept their calm even in the second half when we did not have much ball for the first 25 minutes.
“I thought the team showed a great attitude to go out and play. If you just sit and defend you will get into trouble because Gloucester are too good to let them just have the ball and run at you.
“With the players we’ve got you want them to have a crack.
“Both teams wanted to play and it was probably a good game for then neutral.”
Gloucester scored an interception try in the opening 10 minutes and then turned defence into attack with a counter-attack score on the stroke of half-time to lead 14-13, but three second-half kicks from Flood secured the win for the visitors.
“We probably should have been in front at half-time,” added Cockerill. “But they scored a well-taken try even if it comes from our ball.
“We were quite calm at half-time and thought we were good enough to get the result.
“Then we had virtually no ball for 20 minutes which let them run at us and they got some reward, though they did miss some of their kicks. They put the pressure on us. But we knew if we could get ball and play we could get at them.
“Away wins are important and hard to come by so we’re happy with the points. We’ll take that. We’ve had an important few weeks.
“Now we go into Europe on a decent run. We’ll have two or three more players back and with the injuries we’ve got we dealt with those pretty well.”