Internationals Manu Tuilagi and Toby Flood played big roles as Leicester won 20-19 at Saracens on Sunday to avenge their Premiership play-off final defeat at Twickenham last May and end a Sarries unbeaten home record which dated back to October 2010.
Tigers coach Cockerill said: "Manu had a long lay-off with injury but he's now played two 80 minutes and was still charging for the line at the end, while Floody had a torrid time in last week's disappointing defeat at Exeter and showed his quality with those penalties.
"England have done well with the guys they have, so how they may or may not fit in those two is, happily, not my problem.
"Manu is a very good lad, very professional. But he's also 20. You make wrong calls when you are growing up and you learn from them. Manu is a lad growing up who is also a very exciting player."
Cockerill admitted he was down to his final unchewed nail as Tigers went through 26 phases to pinch victory with skipper Geordan Murphy's drop-goal.
He added: "I was desperate for the lads to go for the drop - probably about 14 times before Geordan finally delivered. And I think it was apt that he should score the winner.
"It was Geordan who sat the players down in midweek and told them what is expected of Leicester players after last week's performance.
"He then made the call to take the drop-goal and did what all great Leicester players do, he led from the front.
"We could easily have lost - it felt like the Twickenham final, phase after phase - only this time we got the rub of the green, this time we achieved a very good win against a very good side."
Saracens rugby director Mark McCall took defeat on the chin and refused to use the fact that they were without 10 senior players through England duty and injury as an excuse.
He said: "It was a tight, very close game as we tend to have against Leicester. I remember when we won a similar game at Welford Road because Billy Twelvetrees missed a last-gasp penalty.
"There were shades there also of last May's play-off final against Leicester at Twickenham, only this time they got the crucial score with the last kick.
"My own sense of disappointment concerns the fact that we were on their line 30 seconds from time and we needed to be more clever in that sort of situation.
"But I also give credit to Leicester for their ability to work the ball through the phases, despite our tremendous defence, keep it alive and score the winning goal.
"I was also disappointed with us at scrum-time, but we had Schalk Brits and Neil de Kock making their first starts after periods out injured, and they showed their quality.
"When we began this project two-and-a-half years ago we knew there would be periods when players would be missing, either injured or on test duty. So we are not going to use absentees as an excuse for losing.
"We were 30 seconds from beating a very fine Leicester side. I am disappointed we didn't, but credit their performance in achieving that result."
Alex Goode missed his first two shots at goal, but went on to kick 14 points, including the last-minute penalty that looked like preserving Saracens impressive home record.
Throw in a cracking de Kock try, sparked by the impressive Brits, which Goode converted, and Saracens did their bit in a compelling contest.
But with Toby Flood kicking four penalties and Ed Slater making up for his first-minute sin-binning after a lineout offence by scoring the Tigers try, it was left to Ireland full-back Murphy to keep his nerve and deliver the killer drop-goal with the final kick of the match.
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