Stephen Ward headed a last-minute leveller for the Seagulls to deny Eddie Howe's men victory at the Amex Stadium and keep the hosts in touch with the play-off hunting pack.
The Cherries, who took a first-half lead when striker Lewis Grabban converted a spot-kick, were denied a club-record third consecutive away league win in the Sky Bet Championship.
Howe admitted Bournemouth were fortunate to be awarded an early penalty, which was coolly converted in the 14th minute by Grabban.
Inigo Calderon appeared to win possession after a last-ditch challenge on Marc Pugh.
"Our performance was good and I am happy because when you hit the post three times and have 10 chances to score you can't be angry or sad," Garcia said.
"Everybody saw what happened with the penalty decision. We had to manage the game differently after that. But it is normal for the referee to mistakes.
"They tried to play higher in the first half, and in the second they sat back which made it harder for us. We deserved to win."
Garcia revealed no discussions have taken place with midfielder Liam Bridcutt about his future, with Sunderland plotting a move to land the 24-year-old midfielder.
He added: "He is a Brighton player and we want to keep our best players. There have been no discussions with him.
"I am a positive person and my thoughts are only about the match. I always thought we would score and that we would get the goal."