The Foxes edged a tight encounter at the King Power Stadium on Thursday, with Nugent glancing home the only goal of the game eight minutes from time.
The one-cap England international had gone 16 games without a goal heading into midweek, but has now taken his record against Watford to seven in 10.
Nugent is looking for Leicester to go to Vicarage Road on Sunday and preserve their narrow advantage, booking themselves a day out at Wembley and a shot at a return to the Premier League.
He told Sky Sports: "It's massive to take a lead into the second leg on Sunday. It was a close game all around. We started the game really well, but we got a bit tired and Watford had a few chances.
"It's going to be tough. When we played them away last time they beat us 2-1. We know they are strong at home and score a lot of goals. If we play like we did tonight, I'm sure we'll have a chance of making the final."
Watford were denied automatic promotion on the final day of the season, but Almen Abdi insists there will be no heads dropping inside their camp ahead of the second leg.
He said: "It was a tough game. We knew it would be before. It's half-time at 1-0 and we play at home on Sunday with everything in our hands.
"I think they played better today, it wasn't our best performance.
"We were mentally a bit down after Saturday's game, but it's another chance for us. We will give 100 per cent until the end and it's not over, we can score a goal at any time."