Tigers scored four tries in beating Northampton Saints 37-17 in front of a crowd of 81,709 at Twickenham on Saturday.
It was the club’s ninth successive Premiership Final appearance and a first league title since 2010.
“First of all there is just a sense of relief,” said director of rugby Cockerill at the final whistle. “As a coach you just want to get it done and win.
“But above everything I’m thrilled for the players.
"People talk a lot about the club’s rich history, we walk about all the great names who have played for the club – like Martin Johnson, Neil Back, Dean Richards, Peter Wheeler – and today it is about this 2013 team, this group of young players who have won the Final.
“These players have battled through and done some great things, and now they’ve come through the biggest game of the season and won it.
“I wanted them to do themselves justice and today it is all about this team – the Coles, Parlings, Youngs, Tuilagi, Allen, all the guys. They have all set their mark in history of the club.
“If you get to the final and lose, it is tough, we know. But this is our year now.
"The club has been around a long time, so many fantastic players have come before this group and now this group is making its own but of history. That is important at such a big club.”
Niall Morris, Graham Kitchener, Vereniki Goneva and Manu Tuilagi shared the tries for Tigers who led 10-0 early on and 16-5 at half-time but had to resist a fightback from Saints which featured tries from Stephen Myler, Ben Foden and Lee Dickson.
“We worked very hard, we played well and Northampton are a good side. We never doubted how good they would be,” said Cockerill.
“Even one man down, they pushed us. They came at us in the second half, it was backs-against-the-wall at times, they scored a good try and it was ‘game on’.
"I said three or four weeks ago this Saints side was good enough to win the competition, they are a good team and the reason we have done well against them recently is because we treat them with a huge amount of respect.
“We’ve played a lot of rugby this season, we have played half the season without our best players, we have issues and just get on with it. It is disappointing to lose on the final day, we have done that more than once, so it is great victory for us today. It is about the players and supporters.
“I thought Logo Mulipola was outstanding for us in the scrum, Anth Allen was fantastic, especially with Toby Flood having to leave the field so early, his experience and knowledge were important. We didn’t play perfectly, we made some mistakes, but these games are about winning.”
