The Hornets have now lost ten Premier League matches in a row at home, falling to defeat on every occasion at Vicarage Road since their win over Manchester United in November resulted in Ole Gunnar Solskjaer getting sacked.
Pontus Jansson’s 95th-minute winner gave Brentford a 2-1 victory, which leaves Watford six points off 17th-placed Everton having played two matches more.
Brentford took an early lead when Christian Norgaard slotted the ball home from an unmarked position, before it was cancelled out by Emmanuel Dennis’ strike in the second half.
However, despite Jansson’s late header securing victory for the visitors, Hodgson insisted the Watford team must not give in.
“One has to believe, one has to keep faith, one has to take some sort of heart from their desire and commitment and effort during the second half,” the Hornets boss said.
“You just have to hope that six times 95 minutes more, they’ll be able to do that and maybe, who knows, we will pick up points we aren’t expected to and we will get ourselves back in the race.
“But it’s not the right moment in time to start predicting that from the next game onwards we are now going to sweep the board and kill all opposition that we find in front of us, because if I say that people will laugh at me.”
The result leaves Brentford just one point shy of the coveted 40-point mark and crucially, 15 points clear of the drop zone.
Bees manager Thomas Frank praised his side’s mentality and how far they have come this season.
“It’s been in many ways a crazy season for us, remarkable season, we are now on 39 points, try to keep focused on winning the next game and finishing as high as possible,” the Brentford boss said.
“With coming up through the play-off final, lowest budget all of that, I think we (must) remember to say that on a day like this.
“On top of that and then we managed to have that, it’s been nearly three years since I’ve been in charge of the Bees and I can’t remember a last-minute winner and we have had three this season and we had more goals where we scored in the last seven or eight minutes.
“We’ve scored 13 goals in the last 15 minutes this season which are remarkable stats and shows two things, that we are unbelievably fit as we keep going throughout the game and the character and the mentality of the group of players is remarkable.”
Additional reporting by PA Sport.