His side were two down after just 12 minutes after Brett Pitman slammed home two penalties but Boro battled back to level through Kei Kamara and Mustapha Carayol before the break and they took the lead in the second half with a Grant Leadbitter strike.
But Bournemouth plundered a point late on as Boro's Jonathan Woodgate turned a cross into his own net.
It followed a 3-1 defeat at Ipswich and a 2-2 midweek draw at Nottingham Forest in which they let slip a two-goal lead.
"We can't keep conceding goals," he said.
"You can't give away three goals at home and expect to win. That's eight in three games now and that is far too many.
"We actually did very well to come from two down to get into a winning position playing some very good football but then we have shot ourselves in the foot.
"We didn't defend well enough. We gave away two penalties and an own goal. No one is happy with that. Something has to change.
"Defending is all about the fine detail and the decisions you make. We can't keep doing this because you can't give goals away and win enough football matches to be where we want to be."
Delighted Eddie Howe praised his side for snatching a point having lost their early commanding lead.
"It was an excellent performance," he said.
"I'm certainly not going to complain about losing the early lead because Middlesbrough are a good footballing side and we knew it would be hard and that anything we got here would be a bonus.
"We got a great start and they came back into it and we showed great character after they got back into it.
"We had to change shape a few times, first to get back into it after they went ahead and then again to shut up shop and I was delighted at the way they applied themselves and did their jobs."
And having taken control with two spot-kicks Howe suggested Bournemouth should have a third.
"The first two were cast iron," he said.
"For me the third one looked clear cut too but no away team is ever going to get three penalties."