A late Tom Bender strike rescued a point for the Saints at Arbour Park and they now sit four points adrift of seventh-placed Billericay.
And despite the fact his side haven't registered a win for three games, Allinson is far from upset.
“We know we’ve got to win games of football. Draws are no good for us and we’re trying to be brave as we can without going forward too quickly, too much.
“We’ve got a good squad but nobody’s going to give up the ghost while it’s four points and mathematically possible.
“Two wins might change everything,” he added. “We’re at home and hopefully we’ll get a decent crowd.
“We know what we’ve got to do. We’ll plan and prepare properly and hopefully pick up three points against a difficult and good Chelmsford side.”