Watford came from 2-0 down to stun West Ham 4-2 at the London stadium.
"I'm very, very happy, particularly because we won a game that we were losing 2-0 against such a big team and in such a big stadium," Mazzarri said.
"For sure this gives a lot of confidence to the players and the whole team. I'm a new manager here at Watford, but slowly we are going to build great things."
West Ham seemed destined for a comfortable win until Ighalo's 41st-minute strike launched Watford's fightback, but Mazzarri never gave up hope of producing an unlikely upset.
"I always tell my players to not think so much about what has happened, but to think about what they can do. I'm very happy my players have this mentality," he said.
"Another concept I tell my players is that they must believe they can win, always, until the referee blows the whistle for the end of the game."