Will Davies' brace gave Sutton the lead in a bleak first half for York, before Dipo Akinyemi gave City hope with a late consolation.
In the end, Geoff King was shown a red card in the aftermath of the final whistle, leaving the Minster men frustrated and unable to take anything from the match.
Coach Hinshelwood refused to make excuses for the performance but questioned the mentality of his players after they failed to show the necessary passion in the first half.
The frustrated York boss made the following assessment:
“I told the players before that everyone talks about how they want the results to go, but if they can't stand up, it doesn't mean anything.
“For the first time in a while, especially here at home, we were way off in terms of competition in the first half.
“We talk about our style and how we want to play, but if you're not going to play on the other side of the game, it doesn't matter and we didn't do that enough.
“Corners, we don't concede too many goals from corners, but it was just the ball going into the box and it looked like the other player wanted to win it. He's obviously at the club and he's a bit hungry. I play by feeling it.
“I keep saying this to my players, and I know people will laugh at me the more I say it now, but that frustrating mindset when you're not playing in a team needs to be instilled from the beginning.
“He has that mindset because he's playing against his old team and that's what it is at this level. You have to play with a little bit of frustration and that wasn't the case in the first half.
“I was really disappointed when they scored that second goal. When you're playing at this level and you lose 2-0 like we did, it's a mountain to climb.
“We have no excuses at all.
“We haven’t seen that much, but at this level you have to be instilled in competing and fighting.
“If you don't do that, you're making it easy for the opposition, and that's what we did today.
“It will probably be looking at team selection and shape, but obviously it's my job to look at that.
“But whenever we get a chance, the players come back.
“Dipo tried to score the second goal here, but it bounced into the channel and made it 3-2.
“Their players are going to show more hunger, show a desire to go all the way, go after lost causes and ultimately score from there.
“If we allow that to happen, we will be in big trouble.
“You can't be too critical of the players because they've been great all season, but you can be very critical of the starting 45 today because it's not up to the level we've set. Because it wasn't even close.”
The referee became the center of attention for the match, with City supporters expressing their displeasure with the referee on display at the LNER Community Stadium.
Yorke became a victim of his own frustration as Dipo Akinyemi, Josh Stones, King and Tyrese Sinclair were shown cards, with a scuffle leading to King's sending off in the aftermath of the full-time whistle. there were.
“I thought his performance was kind of sitting on the frame a little bit,” Hinshelwood judged.
“He stayed away from a lot of the action and when he had to make a decision he always took the easy option.
“We don't blame the two weeks off and we don't blame the referees either. We'll take full responsibility for not doing enough to look at ourselves and try to improve for Tuesday night.”
“To be honest, that’s not what I want to see. I want to see the passion when you can do something right from the start of the game.
“It's not a good idea to do that when you're down 2-0 or when you're 2-1 and have a chance to come back into the game.
“It’s starvation and the idea that you have to pay to begin with.
“I think the players look at me and laugh because I keep drumming for them, which is very important.
“Making stupid reservations and reacting to things is unprofessional and that's not what I want to see.
“I want to see our discussions take place on the football pitch and I don't want it to creep into our game during the 90 minutes.”
