Swansea's winless run was extended to eight matches and they stay in the relegation zone two points from safety.
But former United States boss Bradley, who was in charge for the first time at the Liberty Stadium, said he had been encouraged after Swansea had the bulk of the chances without breaking the deadlock.
"I thought the second half was strong, I liked the way we came out," Bradley said.
"There were a lot of positives, the first clean sheet in a long time, and there's things to build on.
"We're also going to be honest and say we're disappointed we're only taking a point.
"At this point we have to trust the fact if we work the right way, our football gets better, we compete better and do all these little things to improve the points will come.
"As we were going through the second half there were a number of occasions I thought 'here it is'
But when it doesn't come I don't want to forget the things that were positive.
"The reward didn't come in the way of three points, but it's not going to stop the work that I've seen in the last few points."
Bradley made a bold selection call by making five changes from the side which pushed Arsenal all the way in losing 3-2 in his first game at the helm.
The American handed 22-year-old Alfie Mawson, signed from Sky Bet Championship club Barnsley in August, his Premier League debut and was rewarded with an impressive display in central defence alongside Dutchman Mike van der Hoorn.
"Mike and Alfie gave us positive play in the centre of defence," Bradley said.
"Watford is clearly a very different team than Arsenal, and against guys like (Troy) Deeney and (Odion) Ighalo it was a good way to go.
"Alfie has earned respect from his team-mates, day in and day out, and he has a presence on the field for a young defender.
"He is not afraid to talk and organise, he is a solid passer, and I am very pleased with his first game
I've just got to keep these guys facing forward."
Watford have now lost only one of their last six games and this was their second consecutive clean sheet.
"I am happy with the point and the first-half performance, considering it was an away game," said Watford manager Walter Mazzarri.
"The only thing is we should have scored.
"In the second half we made some mistakes and allowed Swansea to be dangerous.
"When we play away and don't manage to score, the home teams grows in confidence
That's what happened.
"We have proved that we are a good team and Burnley (when Watford lost 2-0) was one episode.
"We are growing in personality as a team, but we have to play for the whole game, not just one half."
Source : PA
Source: PA