Boston United coach Joe Simpson confident United will keep up their progress
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Keaton Ward's 48th minutes strike secured all three points for United.
Cameron Gregory made an excellent save to deny Joe Hanks - but City, who had Danny Wright sent off late on, rarely threatened against a well-drilled United side.
“Were were excellent,” he said. “We scored at a very good time and then found a way to keep them out and limit their chances
“At any level you won’t dominate a game for 95 minutes. Teams will have a ten minute spell and it's important to ride the wave out and we did today.
“It was a deserved three points. We haven’t got a right to beat anyone, you have to go and earn it.
“No one will give you a freebie. We are going to make mistakes and lose games, but we are going to get better. We have already beaten some good teams.
“Everyone wants this club to do well. No-one means to make mistakes and we have lost games we should have been out of sight.
“There will be ups and downs, but we want to create a winning culture.
“From where we started 13 months ago, to where we were in summer, to where we are now, there has been progression and we will keep getting better.
“I trust this group and what we are trying ro go. Hopefully as we grow we can create something, not just as a first team but as a club.”
Ward, along with Brad Nicholson, had been recalled to the United side.
Kelsey Mooney header over in the sixth minute, before Zak Mills had a shot kicked off the line by Ben Richards-Everton.
Keziah Martin was denied by a Louis McGrory block, who was forced off shortly afterwards following an accidental collision with team-mate Tyrone Duffus.
United edged ahead three minutes after the break, with Ward beating Zach Jeacock with a powerful drive from the edge of the penalty area.
Jeacock subsequently saved well from Mooney, while Gregory excelled on the hour mark to deny Hanks.
United held on without too many scares - and City's afternoon was compounded in the final minute when Danny Wright was sent off for throwing an arm.