United had to settle for a point despite creating a number of great opportunities. Bournemouth skipper Lloyd Kelly hit his own crossbar with a clearance, Morgan Gibbs-White saw a one-on-one saved by Mark Travers and then Filip Uremović missed the best chance of the lot, deep into injury time.
Gibbs-White also saw what looked a certain penalty decision turned down after being fouled by Nat Phillips.
And Parker, whose side remained second and on course for promotion to the Premier League, said: “A good point in the end, really.
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“I thought it was a well-fought point in a top game . I thought we were the better side for the majority of the game and it’s fair to say Sheffield had the better chances, so on balance of the chance they had the better ones.
“I thought we were very good. It’s been a tough week for us; the turnaround was pretty remarkable really from the West Brom game [on Wednesday night] and then to come to a place like Sheffield, with the intensity and atmosphere and the quality of the team, it’s a tough place to come.
“And in the circumstances, my team were proper today and I’m very proud of them. I thought defensively we were superb and the only element of improvement would be to have some clearer chances.”