The west Londoners are currently sitting bottom of the Premier League table and without a victory in their opening 11 matches.
Mark Hughes' men hope to bring that run to an end when they welcome 19th-placed Saints to Loftus Road and Granero is aware of how important three pints would be.
"We know this is going to be massive for us," he told the club's official website.
"We play at home against one of our rivals. We know the supporters are with us and they deserve more than we are giving to them.
"All we can do is continue training hard and give everything on the pitch on Saturday."
Granero has also been quick to dismiss talk suggesting he could leave the club as soon as January.
"I believe the first win will change everything," he added. "We are doing the correct things and that is why I think it's going to be better for us very soon.
"The beginning has been a little bit tough but I am sure it is going to get better soon.
"Am I happy here? Yes, more than ever. I came here for a challenge and this is what I have."
The former Real Madrid star added: "I wanted to face a big challenge with this club.
"It is a club with a lot of ambition and it wants to grow. I want to grow with it. Together we can move forward at the same time.
"I know the future is going to be good. Of course words mean nothing in football but I will say that we are training very hard for Saturday's game and we are ready."