Minutes later Jamie Vardy fired the Foxes level from the penalty spot after Chris Lowe brought down Andy King.
Yet David Wagner's side will feel mightily aggrieved Kachunga's second-half header was wrongly ruled out for offside – something Shakespeare agrees with.
"We have had it go against us and probably this went for us," admitted the Leicester City boss after the game.
"If you had offered me a point at half-time I'd have snapped your hand off.
"First-half performance we were second best and you have to give credit to the home team, the way that they applied themselves.
"We had quite a few players off the pace but ultimately, at the end of the game when you assess it as a manager, we've played a lot better than that this season and got nothing.
"So to get a point, I have to be relieved and pleased really. You have to pay a lot of credit to Huddersfield Town.
"You could see, in terms of the momentum, what they were about and they will be disappointed they didn't get three points."