Ford, IRB Junior World Player of the Year, kicked four penalties as the Tigers won 17-16 at the Recreation Ground to crush Bath's hopes of sneaking into the Heineken Cup by the back door.
He celebrates his 19th birthday just two days before next Sunday's final against either Northampton or Scarlets.
Cockerill praised the attitude of his team, made up largely of youngsters like Ford and fringe players, as well as others coming back from injury.
"I'm delighted with the result," he said. "The performance was far from perfect but our attitude kept us in there. Bath are a good side and they play a good brand of rugby - if you let them."
Cockerill added: "Fordy does some great things with ball in hand and his knowledge of the game is first rate, far beyond his years. I've wanted to see him play at this level. He's come through with flying colours.
"It would be pretty cruel to leave him out of the side now. I'll play him next week."
And Cockerill said he had no doubt about the effect the win would have on the whole club.
He said: "The confidence and spirit in the squad will be hugely advanced by what we did tonight."
His Bath counterpart, Sir Ian McGeechan, was left ruing his players' wastefulness when they dominated large parts of the game.
"We just had to be more accurate," he said. "We had the opportunities we expected but made errors at critical times. In a close game, any opportunity counts."
He added: "It's always a blow when you lose in the latter stages of a competition. Apart from a scrambled try, Leicester didn't threaten our line at all and, having gone behind, we did really well to get back in front."
On the winning penalty, reversed in Leicester's favour on the advice of the touch judge, McGeechan said: "The Leicester player was binding on the arm, not our loosehead. I'm pretty annoyed with that, particularly when it becomes the match winner."
However, he said he was not giving up on Heineken Cup qualification for next season.
"We've got a good challenge in our five remaining league games and our game is in good shape."
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