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 were revitalised after the break and scored three times in a seven-minute spell, 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.
"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 added: "We needed a win to get a bit of confidence as we had lost a couple of games and put a couple of bad performances in.
"I said 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."
- Sports & Recreation