"At home we have been outstanding so let's hope now that's our little motivation when we come away," said Rodgers.
"It allows us to grow in confidence mentally because tactically and technically we are very strong."
Before Tuesday's trip the Swans had suffered away defeats at Hull City, Norwich City, Leeds United and Nottingham Forest compared to a 100% winning record at home.
But despite the unimpressive away results Rodgers always had faith his team could turn around their form on the road.
"I've never been overly worried, we should have won a few of the games we have had," added Rodgers.
"It was terrific to get the win [at Watford]. It was the win that now pushes us on away from home in particular.
"It was a fantastic performance and result. We have only had one bad performance certainly since I've been in and that was Nottingham Forest.
Give your reaction to Swansea City'sm first away win
"I said to the players that we wanted a reaction [to the Forest defeat] but to still play how we have been playing.
"I thought for the majority of the game we were fantastic. We got three goals and maybe could have had one or two more."
Though the Swans sealed victory they found themselves having to defend for their lives having conceded two late goals and Watford had an equaliser ruled out for offside.
But Rodgers praised the resilience of his players in holding out for victory.
"With 15 minutes to go Watford get the goal which gives them a wee bit of motivation, and then it was different type of game," he said.
Rodgers hails 'fantastic' result
"It was then a battle but I have got to say my guys were magnificent.
"The most important thing was that we put our bodies on the line - because people were maybe looking at us and saying we were fantastic at home, we play great football.
"We come away from home and play great football but we don't win games.
"[It] was a severe examination because Watford have started really well in third position, so to come here was a real test and I thought we passed it with flying colours.
"There's obviously a mental relaxation, you get to 3-0 and I wanted to take one or two players off - Scott Sinclair and Stephen Dobbie who we had nursed through over the the last couple of days and whose contributions were fantastic.
"We have been joking with Angel Rangel that we might not put him on again. He went on at 3-0 and it ended up 3-2.
"We had to stand up and be counted. We were magnificent through the team. We passed the ball well. To a man we were outstanding."
Source: BBC Sport
Source: BBC Sport