The second-from-bottom Cherries are five points behind Grimsby and Barnet, with Accrington 10 clear of the drop zone.
But Coleman told the Lancashire Telegraph: "We can't keep relying on other teams to do the job for us. We're professional footballers and we should be good enough, no disrespect to Bournemouth, not to be getting beaten.
"Bournemouth have the bit between their teeth and I think they've got every chance of getting out of it.
"We just don't want to be one of the ones who get sucked into it. I think if we can get three or four wins in close proximity we can catapult ourselves away from that."