The Union manager was displeased with a yellow card shown to Conor Casey, a perceived lack of protection for the striker, and what he felt to be a foul before New York's winner.
Hackworth felt that New York got away with a foul in the buildup to the winning goal.
"We made a defensive mistake on the goal," he admitted in the post-match press conference, before adding, "For me and for the rest of our staff, there’s a clear foul well before that, and how it’s not called... it’s frustrating."
"[I] just think it's a foul out wide, and then play on, and they come down and get a goal off it, and there were a couple leading up to that."
"I can't blame the officials," he added quickly. "It's our fault, I'm not gonna be a coach that says we lost the game because of someone else, but it is frustrating to feel that way."
Referee Silviu Petrescu showed a yellow card to Union goalscorer Conor Casey in stoppage time when the forward collided with New York keeper Luis Robles.
Asked if he agreed with the decision, Hackworth responded "No. I don't," before adding "Well, it's tough, I haven't seen the replay of it, but what I don't get is how some guy comes on the field and it didn't seem like he was going to get anything, any call going his way.
"There was a play earlier where I thought he got fouled really really harshly. No call. And then to have a couple go the other way, I thought was very inconsistent.
"I have to be careful with what I say so I don't get fined."
Casey, however, contradicted his manager and admitted that he felt he deserved the caution.
"I was tracking the ball and by the time I saw his blue jersey it was too late," he explained. "So, fair enough, it was probably a yellow card."