Kevin O'Connor equalised from the penalty spot of home striker Lloyd Owusu was bundled over by keeper Gary Montgomery.
And Brentford grabbed the winner when Isaiah Rankin forced his way through three defenders before squeezing a shot into the far post.
Harford said: "We started all right, but their second goal saw two of our defenders virtually collide with each other and that is not good.
"We got a bit better in the second-half and we had a golden opportunity to equalise but didn't take it.
"I'm not very happy - we need to get back to the training ground and win our next game or we're going to start sliding down the table."