Town and Bamber Bridge fought out a goalless opening period in front of an expectant 1,549 crowd only for the Shaymen to concede within 16 seconds of the restart.
And Bamber Bridge went to on score twice more as they returned across the Pennines with the points.
"You win games by having a desire and willingness to go the extra inch," said Vince. "On Saturday the players didn't do that for us and I was a little bit surprised.
"I expected better from the quality of players I have got.
"You cannot take it away from Bamber Bridge. They were not as good as us football wise, but they wanted to win the game.
"We were too nice and have to get that bit of nastiness into our game. You have to be ruthless and we weren't.
"The players thought they could just turn up, pass the ball about and win the game. It doesn't happen like that.
"Sometimes you have to take it on the chin and say you were second best, but I didn't think we were.
"There wasn't much between the teams.
"We produced the better football, but they did what you need to win a game - take your opportunities.
"It is very frustrating - and disappointing for the supporters who came out in their numbers.
"We are better than that."
Vince added that he was prepared to give the players the benefit of the doubt after one poor display.
But he made it clear that he will not tolerate any kind of repeat in the coming weeks, starting tomorrow night at Trafford.
"The first one is a freebie from me," he said. "They can have that one.
"Tomorrow I am looking for a reaction.
"I have built a team in a month and I can have another in a month.
"You can do all the coaching, all the instructing, but they have to have the desire and willingness.
"The players have not performed. It was not me, not Nigel Jemson, not the supporters or the chairman.
"We have done everything we can for the players to allow them to show us how good they are.
"They have something to put right on Tuesday."
The hammer blow for Town was the goal they conceded so early in the second half.
Mike Mason was allowed to head home unmarked to start the rot and when Danny Mahoney bagged the first of his double six minutes later it was effectively game over.
"We did all right in the first half and you could see us going on and winning the game," said Vince. "But we were static when we came out.
"Everything I told them to do at half time they came out and ignored.
"It was basic errors that cost us.
"It is easy to point the finger, but the players did not do what they should have done and that's disappointing.
"When you have a dressing room full of quality players they should be performing and should have the desire.
"They showed a bit of that in the last 15 minutes, but it was too late because the damage had been done."
"I am a little bit shellshocked really.
"Bamber Bridge didn't cause us any problems in the first half and then in the second a lapse in concentration in the first minute and we were 1-0 down.
"Within 10 minutes we didn't close a player down and he hit one from the edge of the area."