Bury went into the half-time break 1-0 up after skipper Stephen Schumacher's terrific strike as County struggled to get going. However, the Magpies scored three times in a seven-minute spell after the break, with substitute Francois Zoko grabbing a brace and Jamal Campbell-Ryce completing the scoring from the spot.
And Kiwomya felt the introduction of Zoko at half-time changed the game in his side's favour. He said: "I thought Zoko really made a difference second-half. I thought first-half we played too many square balls and got punished for it with the goal."
He added: "Once we got the first goal the guys thought we can go on and win this. We asked a lot more questions and to do that you need willing runners and we had that second-half, closing down their keeper and running 40 yards to close down a ball which we did well."
Kiwomya said his job at the moment was all about 'steering the ship forward' and he was just relieved to get three points.
He said: "We needed a win tonight to get a bit of confidence as we had lost a couple of games and put a couple of bad performances in. I said yesterday that we needed to get the win first before we could start thinking about closing the gap on the top six and this gives us the confidence to think we can break in to that top six."
Bury manager Kevin Blackwell admitted his young defenders' mistakes had proved costly but with a transfer embargo preventing him bringing experienced players in, he said such errors will happen.
He said: "That six or seven minute period (when County scored three goals) we went all over the place. Young Ashley (Eastham) didn't play well and made a mistake but he's 19-years-old and I said to him, if you want to be a pro you're going to make mistakes as a centre-half.
"Unfortunately he had young Ethan (Ebanks-Landell) beside him at 19 so there was no help for him. We've been embargoed for too long now and we can't bring players in which makes it very difficult. Finances are tight and you end up having to get 19-year-old's to do a man's job and today we got undone.
"It's tough. I admire the work the director's are doing trying to turn the finances around but it's tough for everyone at the moment."