Darryn Stamp’s solitary strike ended City’s unbeaten start to the season, and Housham told the Standard it was a weight off his shoulders.
“It’s the first home win since March and it’s been on the back of my mind for a while,” he said.
“They’ve obviously come with a game plan and tried to slow things down but we’ve kept patient and got the rub of the green and got the goal we deserved.”
Trinity were the better of the two sides in a poor first half, which saw the visitors fail to register an effort on goal.
The first chance of the game came in the 20th minute when Shane Clarke’s low drive from 25 yards was gathered, at the second attempt, by Worcester City goalkeeper Glyn Thompson.
The home side had further chances through strikers Paul Connor and Stamp, and also from on-loan Lincoln City forward Bradley Barraclough, but they failed to open the scoring before the half-time whistle sounded.
Gainsborough came out and started the second half strongly and Connor came close to opening the scoring within five minutes of the restart.
He collected the ball with his back to goal on the edge of the area and, after a good turn, struck an effort that he was unlucky to see crash back off the inside of the left-hand post.
Worcester finally had their first effort on target midway through the second half when midfielder Gary Mills drove towards goal before drilling in a low shot that was saved well by Jan Budtz.
The visitors then finally started to get a foothold in the match for the first time and Danny Glover saw a shot parried to safety by Budtz in the 73rd minute.
Worcester came close again five minutes later when Mike Symons drove in a low cross that was almost turned into his own net by Trinity centre-hal Luke Waterfall.
The deadlock was finally broken with just seven minutes remaining as Stamp forced the ball home from just two yards after a goalmouth scramble following a Trinity corner.
“We got our rewards for a grinding performance,” said Stamp. “We didn’t really have many clear-cut chances.”
“I knew the keeper was right behind me (for the goal) and I’ve twisted and luckily scooped it into the net.”
Gainsborough Trinity: Budtz, Roma, Wilde, Waterfall, Hone, Clarke, Barraclough (Knowles 60), Banks (D’Laryea 90+), Connor (Yates 75), Stamp, Hawkridge. Not used: Young, Nelthorpe.
Worcester City: Thompson, Weir, Deeney, Thornley, Whitehead, Rowe, Reece (Edwards 58), Elvins, Symons (Taylor 81), Glover, Mills.Not used: Ayres, Denny, Sargeant.
Referee: Jason Tyas (West Yorkshire).