"He's one of those characters who, the more criticism he gets, the more determined he becomes," Moores told reporters.
"He just gets steelier. He would openly admit that he's had a really tough ride. But that often can forge somebody into something special," he added.
After England lost at Lord's, more than a couple of weeks ago, Cook had presided over a run of 10 Tests without a win, including seven defeats.
Cook had then admitted his position as England captain was under pressure.
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Quite a few former England captains called on him to resign and some even went as far as to suggest the opener take a break from the game after a run of low scores.
Their confidence restored, England then thrashed India by an innings and 54 runs inside three days to win the fourth Test at Old Trafford, thereby taking a 2-1 lead ahead of next week's final match at The Oval.
"He is developing quickly as a captain tactically and has great values to lead with from example," Moores, in his second spell as England coach, said of his skipper.
India lost nine second-innings wickets after tea on Saturday, and that too in the absence of England pacer Stuart Broad. Broad was off the field after suffering a broken nose while batting.
"We had seen a lot of the younger players do well, but the fact that the senior players have really performed well over the last couple of games has really added something to us."
Moores added: "We have won two Tests but we have got to be pretty careful we don't get carried away.