The Blades, who were at a similar level on Tuesday evening as they lost 2-0 at Middlesbrough, make the long trip south looking to rediscover the form that had seen them go five league games unbeaten before being undone by Neil Warnock’s men.
Bournemouth’s top scorer Dominic Solanke missed two late chances to win the game at Peterborough, but he shot and headed over as Posh held on for a precious point.
It saw Bournemouth miss the chance to re-take top spot in the Championship and Parker said of his side’s performance: "It was a bit passive. We lacked intent and played the game in front of them.
"To their credit Peterborough are an organised team and limited the space.
"There was a reaction in the second half and we had an attacking threat. We've just not managed to put the chances away. We gave ourselves 45 minutes to win a game of football and that's not us.
"We've been very clinical and very fluid (previously) but we've not put the ball away. We had some good chances but looked a bit off it. That's football. They're humans and sometimes have those moments.
"The second half is where we need to stay.
"Dom's been fantastic since I've come here and missed some chances, but he puts himself in good areas for the team. It was just not his night."