Grabban appeared to dispossess Middlesbrough goalkeeper Dimitrios Konstantopoulos as they competed for the ball on the edge of the penalty area.
Konstantopoulos seemed to lose control and Grabban drove his shot into the vacant net for what could have been the winner, only to see a foul called.
Howe said: "I did not think the keeper had the ball in his hands. Grabbs had every right to go for it and I have to say I am disappointed with the decision of the referee for disallowing it.
"We did everything we could to win that game. Middlesbrough were dogged opponents that didn't come out their shells, as their recent record shows in terms of defensive performances.
"It shows how far we've come this season that we are saying that we are disappointed only to draw with Middlesbrough.
"They showed us a lot of respect. We knew we would have to be at our best to break them down and we did not look like doing so often enough. We did not have that elusive chance.
"Defensively our performance was flawless. Lee Camp, our goalkeeper, did not have much to do and for that we must play tribute to the players in front of him.
"We did not let Middlesbrough into the game but with two outstanding wingers they could have hit us on the break and won the game."
Middlesbrough's draw was their fourth without a goal in six matches, and their 11th clean in the last 16 league fixtures.
He said: "We need to do more, we need to play better. (How) one team can play how we play at home and (how) we play away, it's difficult for me to understand why.
"I want to thank the fans who have come 300 miles across the country to watch this and I would have like us to have rewarded them with some goals.
"At least we have a point. Bournemouth had more chances and played very well, so we have to be pleased with that."
In a match of few chances the best opportunities fell to Bournemouth who were seeking their fourth successive league victory.
Konstantopoulos made two outstanding saves in the second half, flying to his right on both occasions to keep out shots from Simon Francis and Andrew Surman.
Middlesbrough's best chance fell to Lee Tomlin in the 43rd minute, but the former Peterborough volleyed over from 15 yards after being set up by a Carayol pass.