Tigers ran in 27 tries in wins over National League One opposition Cornish Pirates, Bedford and Nottingham, then beat French duo Bayonne and Montauban in preparation for the start of the Premiership title defence at Bristol on Sunday.
Tom Varndell, Tom Croft and Matt Cornwell were among the try-scorers in Saturday's 32-10 win over Montauban at Welford Road and, although Cockerill admitted the performance left room for improvement, he welcomed the unbeaten run.
"We have won five from five and we have shown a spirit that you cannot coach," he said.
Cockerill and the players now have a full week's training before the season's big kick-off at Bristol's Memorial Stadium.
"Bristol is a difficult place to go, but we are looking forward to going there and seeing where we are at as a squad," he said. "I know the players feel they really need to play a big game and we have certainly got that next weekend.
"It was a pretty ordinary performance in many ways on Saturday but we defended exceptionally well. We are not perfect but there are positives to take out of the game, including the work at the scrum and some of the line-outs. It was also a relatively good debut for Christophe Laussucq and some of the younger guys stood up.
"We got an early score and looked sharp but just did not have the edge to our game that we would have liked."
