In front of a large crowd, featuring a number of travelling Tigers supporters, the visitors took the spoils thanks to a converted Tom Varndell try and Paul Burke penalty, but it was the spirit of the team that particularly pleased Cockerill.
After scoring 27 tries in the previous pre-season wins over Cornish Pirates, Bedford and Nottingham, it was a lot tighter in Bayonne and Cockerill said: "It was not a pretty game, that's for sure, but the boys dug in and got a win.
"You cannot coach determination and commitment, and the lads showed that by the bucketful.
"We came away to France and won, which is always difficult, and you could see why teams do not lose many games at home over here.
"We have always been on the front foot in our other matches this summer, but you know you are going to have to play on the back foot too once we get into the season and we showed we could do that. We defended exceptionally well."
With the final warm-up match against Montauban at Welford Road this Saturday and the Guinness Premiership kick-off to follow, Cockerill said there was still work to do.
"The performance in Bayonne showed that perhaps we are not as good as we think we are, which is not a bad thing in some ways," he said. "There is still work to do. We created a lot of opportunities in the first half and did not quite take them."
Tickets for the visit of Montauban to Welford Road on Saturday (3pm kick-off) are on sale now. Contact the ticket office on 08701 28 34 30.