The gaffer said Tuesday night provided a fair result on a night of "mixed emotions", which he described as a great advert for the Northern Counties East football League.
After going 2-0 up thanks to top scorer Ross Duggan and debutant striker Jack Warner, Luke Francis's second half brace dragged hosts Handsworth back into the tie and earned his side a point at Sandy Lane.
Although the Bulls had surrendered a two-goal lead, the boss refused to call it two points dropped: "A wise man always told me: three points at home, one point away and you'll be happy come the end of the season.
"For us we had zero points when we walked into it, we've come away with one point and I think it was a fair result.
"It was a game of two halves - I think we had a chance in the second half to kill the game and finish it.
"Silly errors cost us; it's a good side, Handsworth, they've got good strategy on how they want to play... I just think some players had to deal with that better.
"If we dealt with the individual mistakes better, we would have come away with three points."
Despite the late disappointment, there were positives to reflect on, including the perfect start for new signing Jack Warner who provided the goods with a goal early into the second half.
"We threw him in the deep end and gave him a start because of personnel being injured," Chatfield said, "we gave him the chance and he's delivered - on the ball he was class, off the ball he worked as hard as he could do and he provided a goal to cement his place."
The Bulls look ahead to a tasty fixture on Saturday afternoon, when they welcome local rivals Rainworth Miners Welfare to the Forest Town Arena for an FA Vase Second Qualifying Round clash.
Chatfield told Bulls TV he couldn't wait for Saturday to come.
"(Rainworth) will be up for it, and I'm sure our lads will be up for it now, especially since tasting the blood of a league game - they're ready for another feisty affair.
"They never give up, they work as hard as they can and that's all I ask of these lads, so I can't wait for Saturday and another exciting game."