Niall Morris and Adam Thompstone scored the tries as Tigers won 32-24 to claim an international victory on an historic evening, but Cockerill acknowledged the efforts of everyone in the camp.
“We kept talking about this being all about the occasion,” said Tigers director of rugby Cockerill.
“You don’t often get that where it is all about the occasion rather than league points or placings or cup qualification. It was up to us to play well and put on a show for the fans.
“We wanted to show that Tigers is a good, strong club and we really wanted to go out and give it a crack. We desperately wanted to play well and win it.
“It was an outstanding effort from the club as a whole, from the Board to get the game on, to the players and the supporters. There is a great pride in being able to say you played for Leicester Tigers against the Maori All Blacks and won at Welford Road.
“Seeing the Haka here, that will be an iconic picture for everybody to look at.
“There was a really good turn-out from the crowd, the support was great, they were very vocal, which was important for the players.
“We really wanted to play well. We had some good young players in there who had their first opportunity to play at this level and I’m really pleased for the guys.”
Cockerill was impressed by the quality of a game which featured five tries, three yellow cards and almost non-stop action.
The Maori claimed the opening try from scrum-half Frae Wilson and scored 10 unanswered points approaching half-time including a try from centre Tim Bateman as Tigers led 26-17.
Their third score, from centre Charles Ngatai, converted by Willie Ripia, reduced the deficit to just five points with 20 minutes remaining, but Tigers were able to close out the victory.
“From seeing Super 15 rugby you know they like to play, there are some big men who can carry and play the ball in contact, and there are a lot of skills in the team,” Cockerill said.
“The first try for them was fantastic play. Sometimes you just have to applaud and say ‘well done’.
“But I thought we managed the game well and the defiance in defence was excellent, especially when we were a man down after Dan Bowden’s yellow card. The willingness to keep going at them and not panic was important.
“It was a great night and I’m just delighted for the players.”