Borough also had striker Tony Lee sent off five minutes from the end following a scuffle.
Player-manager Craig McAllister was happy to avoid a second successive defeat but felt it was a missed opportunity.
He said: ‘We were not at our best going forward.
‘It is an area where we have been good recently but not this time.
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‘I thought their 3G pitch might have suited us a bit more.
‘Their goalkeeper wasn’t put under any real pressure.
‘Though it is good to keep a clean sheet and get a point away from home we need to be winning these games.
‘It was a chance for us to put a bit more distance between us and the teams below us.
‘Basically it turned out as a game between two teams desperate not to lose.’
In the first half Borough felt they had genuine claims for a penalty turned down after Lee was sent sprawling in the area.
Both teams went close without making the breakthrough.
The visitors gave a debut to Hawks utility player Josh Huggins who has been dual registered.
McAllister is delighted to swap one Hawks loanee for another after seeing Mike Carter return to Westleigh Park.
He believes Huggins can play a vital role in helping Borough stay up.
The Borough player boss said: ‘Josh did really well for us filling Mike Carter’s boots.
‘He is another experienced leader and the sort of player we need out on the pitch.
‘His experience helps him in seeing games out.
‘I was impressed with his contribution even though he hasn’t played for a while.
‘He is only going to get better and better with regular games.’
McAllister was less happy with Lee who could miss crucial games in the next couple of weeks.
He said: ‘I didn't see the incident but apparently our player raised his hands and you can't do that.
‘He didn't need to get involved and should have known better.
‘It summed up his frustrating afternoon.
‘Losing him for the games coming up is something we could do without.
‘It remains very tight at the bottom and it is obviously going to go to the wire.’