Tigers claimed an 11-8 win at Welford Road after coming from 8-3 down in the second half.
Director of rugby Cockerill said the performance was very disappointing and that the win was “one of the only positives” to come out of the game as the squad begins preparations for two important road trips.
“It was a poor performance, we did not play well across the board, there is no escaping that,” said Cockerill.
“We created scoring opportunities but turned over ball far too easily and if you do that you keep the opposition in the game. Gloucester were dangerous in attack and scored a very good try while we struggled to get our game going.
“We were hanging on for dear life, but we came through, we take the win – it was probably the one positive from the game.”
Tigers had to dig deep, trailing 8-3 with more than an hour gone, before patiently creating an opening for Tait to claim his first try of the season and then provide a platform for Toby Flood to kick the winning penalty.
“We really only started to play when we were in danger of losing the game,” said Cockerill. “In the last 10 minutes we got a bit of intensity, kept hold of the ball and managed to put them under a bit of pressure. And we scored our try. We just didn’t do that often enough.
“Everybody is working hard but the lack of accuracy was disappointing.
“But we did get the win in the end and we live to fight another day. Looking at some of the results over the last couple of weeks, it is very close in this league and we’ve come through with two wins even though we have been disappointed by the performances.
“We’ve now got two games on the road against sides fighting to get themselves up the table and we have to be better.”