Substitute Dan Hipkiss scored the winning try three minutes from time as Leicester edged out Saracens 33-27 in a Twickenham thriller.
"To win back-to-back titles is hard, very hard, and you have got to give the players a huge amount of credit," said Cockerill.
"Games like this one are cracking matches - as long as you win them.
"Saracens could have won the game - if they had won, people couldn't have said they wouldn't have deserved to."
Hipkiss followed centre Matt Smith and scrum-half Ben Youngs over the Saracens line, while fly-half Toby Flood kicked 18 points. Saracens replied with an Ernst Joubert try double and 17 points from Flood's opposite number Glen Jackson.
Hipkiss' score came when Leicester gathered possession from Flood's restart after a Jackson penalty, and Saracens were finally finished following an epic tussle.
"I wondered how we would win the ball back," admitted Cockerill.
"But Floody kicked it in the right spot, Scott (Hamilton) caught it, Danny finished off and we won the game."