The Hornets are six points from safety.
The second-bottom Hornets slipped six points from safety following a ninth successive home loss which manager Hodgson termed “harsh”.
Raphinha’s first-half strike set Leeds on course to move nine points clear of the drop zone before calamitous home defending helped Rodrigo and Jack Harrison kill off the game at Vicarage Road.
Hodgson has now lost seven of 11 games since succeeding Claudio Ranieri in January and faces a major salvage operation to prevent the club’s immediate return to the Championship.
“I’ve never used the word confident; I don’t want to set myself up for headlines or statements which I can’t identify with,” replied Hodgson when asked about survival hopes.
“We have no reason to be confident. We do have reason to believe, we do have reason to have faith, we do have reason to think that we aren’t that bad and results are still a distinct possibility for us – we’ll keep doing that for sure.
“But to suggest that by saying that I’m now saying: ‘I am confident’ (is not true).”
Watford’s day began badly with news that fellow strugglers Everton had registered a surprise 1-0 win over Manchester United in the lunchtime kick-off.
Their position could become even more perilous by the end of the weekend with rock-bottom Norwich due to host 18th-placed Burnley on Sunday.
“I don’t think anyone at Norwich or Burnley will be saying that; I don’t even think Everton will be saying ‘we are confident’,” he continued.
“But what Everton have got today and what Leeds have now got in the last four games, they’ve got results and they’ve given themselves a very, very strong margin, which makes their position so much better than ours.”
Raphinha’s 10th goal of the season fired Leeds into a slender half-time lead before Hornets forward Ismaila Sarr wasted a golden chance to equalise with an hour gone.
Rodrigo rounded Ben Foster to add a crucial second 17 minutes from time after Hassane Kamara catastrophically played the ball against team-mate Samir, before Harrison rubbed salt into Watford wounds late on.
Watford return to action at home to Brentford next weekend and Hodgson has urged his players to swiftly move on.
“It’s frustrating; we wanted it so badly,” said the former England boss.
“The second goal was a real killer blow in a period of the game where I thought we were doing it fairly well.
“What we have to do is find a way of putting this game and this result – which I thought was a very harsh result – behind us and to make certain we don’t allow it to affect too deeply with seven games to come.”
Leeds have now taken 10 points from the last 12 available under head coach Jesse Marsch to give themselves breathing space in the scrap for survival.
“I’m really excited that we were able to in a tough moment and in a really important game emerge,” said the American, who replaced Marcelo Bielsa in late February.
“The points are massive for us and there’s confidence and momentum in the group.
“After six weeks, we can see that the form of many players and the overall mentality of the group has grown so much, so that’s really helped us get to where we are right now.”