The gaffer blamed a lack of desire for the 2-0 NPL East Division defeat at Belper Town on Saturday.
Danny South and Derry Robson notch two crucial goals for the Nailers on either side of a Town red card for Alex Peterson, whilst the Bulls were unable to take advantage while on top.
"I don't think we hurt them enough with our work," Mark Ward said after the game.
"The difference between the two teams was the desire in both boxes, in one to score goals and to keep them out at the other end."
Ward said that the presence of target man Danny South was something his team most certainly lacked: "It's massive for any team.
"When you've got that outlet and presence in good areas all around the pitch, nine times out of 10 you're going to win the battle.
"For 10 minutes after he got sent off we had some good opportunities and we put balls in good areas, and with the extra man we should be making that count.
"But we're putting balls into the box and their centre-halves are getting free headers.
"We had the extra man, so it's frustrating for me that we haven't got players who want to go and stick the ball in the back of the net."
Fans can watch the full post-match interview now on Bulls TV.