Higginbotham saw David Nugent bag a brace for the in-form Foxes, with further strikes coming from Lloyd Dyer, Anthony Knockaert, Martyn Waghorn and Marko Futacs.
"It's disappointing all round and we know we weren't good enough," Higginbotham said.
"It's frustrating to go from a good result (against Burnley) to a performance like that against Leicester.
"We need to get some consistency into our performances and we didn't have that.
"We can't have any excuses and it's up to us, as a team, to take responsibility and turn this around."