Sargent, 21, became a father for the first time earlier this month and his double at Watford helped his side to a 3-0 win that moved them out of the relegation zone.
His first goal of the game came minutes after the release of the USMNT roster announcement for upcoming World Cup qualifying matches, of which Sargent was not included.
Speaking after the match, he said: "It's been a kind of blur. To get your first goal and then your second after was pretty crazy. It was a big game for us so a great night overall.
"Obviously being in the relegation zone means every game is big for us, but to get a win against the team right in front of us is huge."
Sargent had struggled in front of goal this campaign, with his only other strike coming in the Carabao Cup, but he followed up his impressive opener with a header which he celebrated by paying tribute to his newborn child.
"After the first one I didn't celebrate for my newborn baby so I knew the wife would be on my case," he added. "I thought 'I need to do it now!'
"It's been a crazy couple of weeks obviously but I'm very happy. It's been amazing."
The win over Watford was Norwich's second in consecutive weeks and lifted them above Claudio Ranieri's side and out of the bottom three.