Former Manchester United starlet Collett suffered a badly broken leg following a challenge from Smith in a reserve team game in 2003.
Collect was awarded damages last August in excess of £3million as he was forced to quit the game.
Boro and Smith's insurers - who cover the costs of the pay out - appealed on their behalf.
But Lady Justice Smith ruled against the appeal, saying Mrs Justice Swift's ruling in the initial case was correct.
"The judge has put into the balance the possibility that the he might have done better than she had predicted," said Lady Justice Smith.
"She was entitled to take that view."