Matt Ritchie salvaged a draw with the last kick of the game at the Vitality Stadium – but Rafa Benitez felt Newcastle United should have claimed all three points.
Benitez's side held Bournemouth to a 2-2 draw this afternoon.
Newcastle – who had taken the lead through a first-half goal from Salomon Rondon – looked to be heading for defeat after Josh King scored his second goal of the afternoon with nine minutes left on the clock.
Ritchie claimed a point with a stunning volley against his former club, but Benitez felt that his team could have left with three points if they had "managed" the game better.
The result left the club 13th in the Premier League and three points short of Benitez's 38-point safety target.
"Yes, I thought we'd lost it," said Benitez, who was unhappy with a number of referee Mike Dean's decisions.
"Too many things were against us. We had to react, but I thought we did it well.
"It was a great goal from Ritchie, so I'm happy for that, but I'm disappointed because we could have got three points if we'd managed better."
Ritchie – who had had a penalty saved in the previous weekend's 3-2 win over Everton at St James's Park – had to stop himself celebrating out of respect for his former club.
"He has been doing well for us, and he scored a great goal," said manager Benitez.
United, potentially, are just three points away from securing their Premier League status with seven games left to play.
"It's not done," said Benitez. "We have to keep winning games. It could be 38 points, maybe 40 will be a guarantee. Maybe 38 will be enough though."