He says the defeat hurt because the performance lacked the competitive spirit which has been a mark of City's game since winning promotion in 2008.
Higginbotham added: "It is one thing to get beaten, but Bolton thoroughly deserved that win as all of us had an off day.
"We have become renowned for being resolute and hard to beat, so we are a group of lads who take defeats like that to heart.
"Every team has games like that, but it is how you respond to them that is important.
"The lads are frustrated and hurting because we were bad from start to finish. We want to do it for the fans but, as professionals, we also want to do it for ourselves."