Heidar Helguson had the best chances for Rangers but was narrowly off-target with one effort, while Watford keeper Scott Loach made a save to deny him a second time.
Watford came even closer to breaking the deadlock in the second-half when Lee Williamson struck the woodwork with his free-kick.
And new Hornets' boss Brendan Rodgers was pleased with the solitary point against the promotion hopefuls.
He said: "I thought we played well, especially in the first-half and as the game went on, I thought we were going to nick it.
"This performance has shown the gradual growth which we have been trying to achieve.
"I have watched this League from the outside and seen the pressure to get into the Premier League, sometimes the players are better than the football shows.
"My ideas on football are not the typical British style and that's going to take some time to get that across to my players."
