The Manchester side went into half-time 9-3 up through the boot of Nick Macleod before Bath took the lead through Horacio Agulla's converted try. However, Tom Brady touched down late on and, with London Welsh being deducted five points for fielding an ineligible player recently, the Sharks moved six clear of the Exiles.
Diamond said: "We were fortunate to get off the bottom of the league with the thing that happened with London Welsh, but we've done all right at home since Boxing Day. We've been beaten by a couple of the top-four sides and Montpellier but it's (the Salford City Stadium) starting to become a little bit of a home."
He went on: "In the first half I thought the conditions were all over the shop and we won fair and square, and in the second half we had good composure in the last 10-15 minutes.
"Tom Brady came on and scored a good try. There wasn't much rugby played out there but in those conditions you can't really expect it."
Meanwhile, Bath head coach Gary Gold admits that their chances of reaching the top-four have all but ended.
The west country outfit currently reside in seventh position, six points behind fourth-placed Northampton, with their rivals yet to play this weekend.
Gold said: "We came in here today setting ourselves goals and objectives to hopefully be in the top four. That's probably gone now but never say never.
"We'll probably be written off by everybody now so we've got a lot to prove."