Joel Sherman tells us what happened:
Cashman raised the bid twice more early in the evening. He believed by reaching $52 million over four years the Yanks stood in stark contrast to the $40 million the Red Sox would not budge off. Meanwhile, the Yanks also thought the center field and leadoff markets had expanded so much that $13 million annually was a proper figure; Rafael Furcal, after all, climbed to $13 million annually due to leadoff skills.
But Cashman also told Boras that if the Yankees' offer was not accepted, Cashman would very publicly announce they were out of the bidding, which might even convince Boston to lower its bid as the lone team left in negotiations. Instead, Damon accepted without giving the Red Sox an opportunity to match, which left the Boston front office looking stunned and inept. The Red Sox had let an emotional, tactical edge fritter away and, worst of all, let it be the Yankees who stole an immensely popular, productive player.
I watched the Red Sox reaction again and they were completely "dazed and confused."