A goal in each half from Ryan Kendall and Andrew Boyce was enough to see off the struggling Cumbrians.
Housham admitted it was good to make amends after Saturday’s defeat at Hyde.
He told the Standard: “It was good to bounce back and get Saturday out of our system.”
“Tonight we played some good stuff, it was good to watch. I stood there and I enjoyed some of the football we played and there were some good performances out there.”
The Blues have now won six out of the seven games under the former Brigg boss, a run of results that has propelled them into the play-off places.
But Housham refused to give himself credit for those achievements.
“It’s down to the players, I’m there raising my voice as much as I can because I want these players to do well.”
“I want Gainsborough Trinity Football Club to do well. It’s midweek and we’ve got 470 fans here and they’ve gone home happy again and I want to please those fans who have shown a lot of faith in the club,” he added.
Trinity’s victory was their fifth at the Northolme this season and Housham wants his side to maintain their good home form and be hard to beat.
He said: “This is our patch and we don’t want anyone to take anything away from us on the pitch so we’ll be prepared for Saturday.
Goalkeeper Phil Barnes missed the game after picking up an injury in the defeat to Hyde so in stepped debutant Andrew Pettinger who earned special praise from his manager following a confident and assured display.
“I thought he was superb tonight, he made some great saves.”
“He made a great save in the first half, I think he just misjudged the bounce of it and it slid through but he’s recovered well and saved it.”
“I’m pleased for him because he’s come a long way and he’s getting that appetite back for football,” Housham said.
There were two other changes to the side that were beaten 3-1 at Hyde, Rory Coleman also started his first game for the club replacing Workington-born Kevin Sandwith at left-back while Lewis McMahon came in for Michael Leary.
But Pettinger it was who almost had a scare in the opening minutes. After seemingly misjudging a Workington centre, Kevin Gall rounded the former Everton trainee but just as he looked poised to slot into an empty net Pettinger leapt to make a superb diving save to his right.
It took until the 20th minute for Trinity to register their first attempt on target with Jamie Yates forcing Aaran Taylor into a fine save.
Gainsborough managed to break the deadlock on the half hour mark through Ryan Kendall.
Yates’s excellent turn down the left flank found an unmarked Kendall in the box and he fired high into the roof of the net.
Kendall came within inches of doubling his tally within 60 seconds of the restart tucking Jonathan D’Laryea delivery just wide of Taylor’s upright.
Strike partner Darryn Stamp nodded a Williams centre over and the latter came close to grabbing that second goal with a left wing cross that almost looped over Taylor.
Workington’s Mark Boyd volleyed over in a rare attack from the visitors and only the backside of defender Anthony Wright denied Yates’s goal-bound effort just before the hour.
McMahon, playing in an unorthodox midfield role fired wide from range and the visitors crossbar was rattling minutes later through Yates’s deflected shot.
On 68 minutes, Phil McLuckie spurned a great opportunity to level but instead flashed over. And substitute Stuart Green had his head in his hands when he drilled a shot inches wide.
The visitors were punished on 72 minutes when Andy Boyce nodded home his third of the season, latching onto D’Laryea’s cross.
The league’s bottom side came close to halving the deficit with 10 minutes remaining but Pettinger made another great save to deny Jake Simpson.
Visiting full-back Anthony Wright nearly gifted Trinity a third towards the end when his headed backpass had to be clawed from his own net by Taylor.
But Trinity were well worth the points on a wet and skiddy Northolme surface, where they entertain third-placed Guiseley on Saturday.
Gainsborough Trinity: Pettinger; Roma, Coleman, Cowan, Boyce, McMahon (Leary 70), D’Laryea, R.Williams, Kendall (Paczkowski 85), Stamp (Mettam 74), Yates. Subs (not used): Sandwith, Leary, Waterfall.
Workington AFC: Taylor; Smyth (Green 48), A. Wright, May, Wordsworth, Boyd, McLuckie, Hewson, J.Wright, Arnison (McNiven), Gall (Simpson 63). Subs (not used): Main.
Referee: Alf Greenwood.
Assistants: Anthony Murphy, Chris Woodall.
Goals: Kendall 30, Boyce 72.