Norwich have now fallen into the bottom three and with 15 games left Rodgers believes his side have their fate in their own hands.
He said: "It's in our hands now and we play a lot of the teams around us.
"We are better than our position suggests and we are still improving game by game. Hopefully we will stay out of there now.
"That was terrific. It was a very good performance in the first half and tactically we were outstanding.
"They play 4-3-3 and that is a system I know well from my time at Chelsea. We matched them up and we used it well defensively and offensively.
"We were assured and our discipline was outstanding. When you play as a passing side like Swansea do sometimes if you lose it there are big spaces to exploit and that was what we did for the first goal."
Swansea had last been beaten in any competition way back in November and Rodgers was quick to praise the rapid progress made under Roberto Martinez.
He said: "I'd like to put on record that the job that Roberto is doing is outstanding.
"The football that they play is a credit to him and he is two years ahead of where I am here.
"If you play football like that more often than not you will get results."
Martinez felt that the Hornets' display was 'perfect' and cursed his side's failure to respond to the sticky Vicarage Road pitch.
The Swans appeared to manage to play their normal passing game to good effect but Martinez felt they were outbattled by the hosts.
He said: "Everything about Watford was perfect. They were very organised, they worked hard with and without the ball and were clinical.
"They scored with their first attack which came from our corner.
"It was a disappointing performance but we did not have what was needed to win the football game.
"Watford had huge desire and tempo in terms of trying to get three points.
"We are at that stage of the season where the table affects performances and Watford reacted really well to the conditions and deserved all three points."
Martinez left out Angel Rangel and Mark Gower from the side which dominated against Fulham in the FA Cup at the weekend but admitted his squad has been stretched by their exploits.
The Spaniard was unmoved after a first loss in three months and called for a reality check. He said: "We couldn't find any energy but we are playing 10 games in 33 days and that is hard for the human body to withstand.
"I left a few players out but we play in a way that is very demanding and we have to use the whole squad and share the effort. "In football you have to be adaptive and that has been behind the success we had here.
"We have managed to play our own game wherever we have gone but that didn't happen tonight.
"We have to be realistic. Nine months ago we were in League One and now we are expected to win every game.
"Now we need to begin on another unbeaten run."