The Robins, who kept a clean sheet for the first time since April 2012, survived some early scares against the division's top scorers and then took the lead in fortuitous circumstances when Greg Cunningham's hopeful cross found its way into the back of the net.
Paul Anderson scored after a smart corner routine in the second half to secure a valuable three points in the battle for survival and O'Driscoll admitted it was all about getting his side to work on the simple things.
"I've just organised them really," he said. "The previous game before I came in when they lost 4-0 to Leicester there wasn't much between the teams other than the goals.
"You need to be in a position in the Championship to win the ball back as quickly as you can. And if you can't win it back then you need to be in a position to not concede a goal and I just felt in that game we weren't in a position to do either.
"There was no lack of effort there, it was just tweaking it a little bit. They are a good group of players with a willingness to do well. You can speak about it but the players have to do it and their behaviour has been first class."
Watford manager Gianfranco Zola, whose side were seeking a fifth straight win, missed their best chances with the scores level. Almen Abdi fired over the bar before Alex Geijo missed a gilt-edged chance from inside the six-yard box, but Zola was upbeat despite their impressive run coming to an end.
"Losing is part of the game," he said. "You win and do well like we have been recently and then you play a bad game like this. We are not a team who are going to be invincible and will win all the games.
"We were in a good spot and we are going to keep pushing. We know that we need to improve on this, we made some mistakes and we didn't expect them to play in that way.
"That and the lack of quality in the last third has caused the problem. I think what is important is the reaction. Saturday we have a big game and I am expecting a good reaction from the players."