The Spaniard, who joined the Hornets from Barcelona on a loan deal during last month's transfer deadline day, scored in the team's 4-1 win at Vicarage Road.
As well as finding the back of the net himself, Deulofeu won his team a penalty in the first half after getting clipped by goalkeeper Thibaut Courtois.
"We are happy for these three points, the team fight at the beginning and we are worth this win," the former Everton player told Sky Sports News. "I'm so happy for my first game at home.
"Daryl Janmaat gave me a good ball and I think it's a clear penalty. [Courtois] touched me.. I think."
Chelsea played an hour of the encounter with 10 men following Tiemoue Bakayoko's sending-off.