After soaking up plenty of pressure for the rest of the match Carlton was presented with two opportunities at the death.
The match was well into the three minutes being added on when Carlton drilled a shot straight at goalkeeper Shwan Jalal from ten yards.
Then seconds later Carlton was unmarked when he headed a centre from Andy Parrish against the top of the bar.
It would have been rough justice on Bournemouth, who still need one point to get rid of the 17-point deficit imposed on them by the league for going into administration.
Bournemouth had plenty of pressure but little to show for it, to the frustration of the crowd who booed the team off at the end of the match.
The Cherries' brightest spell was in the first half and left-back Warren Cummings had an inswinging corner cleared from the line.
Veteran former England midfield player Darren Anderton had a shot blocked at close range, but the nearest Bournemouth came to scoring was in the 43rd minute.
On-loan Michael Symes saw a right-foot shot rebound from the post with goalkeeper Barry Roche beaten.
Carlton had the ball in the Bournemouth net after 53 minutes, but it was ruled out for offside and Danny Adams got the game's only booking for a foul on substitute Marvin Bartley.
Bournemouth's only clear chance of a drab second half came in the 85th minute when a left-foot effort from Danny Hollands drifted wide.
The crowd of 3,068 was the lowest for a league match in the seven years of the new stadium at Dean Court.