Second-half goals from Albert Adomah and Danny Graham extended the losing streak for Garcia's men, who missed a penalty when trailing 1-0, and left them four points adrift of a Sky Bet Championship play-off spot.
Leonardo Ulloa's badly hit spot-kick sailed over the bar into the home fans to cap a miserable day for the hosts, who have now won only one of their last six home games in all competitions.
"We're making mistakes at the back and we are being punished," Garcia said. "The problem is we are not punishing the opposition ourselves and now these are the kind of things that are making the difference.
"We started slowly, were the better side in the second half but they went in front and then us missing a penalty was a blow. Their second goal was a killer."
Garcia refused to criticise Ulloa for his spot-kick blunder, the Argentinian striker having stepped up with regular penalty-taker David Lopez having been substituted.
"It's a personal decision and you have to feel confident enough," the Spaniard said. "It was a poor penalty but we can't blame Leo - he's scored crucial goals for us."
Brighton were booed off by a section of their fans at half-time and at the end, although Garcia said he had not been aware of any discontent at the interval.
"I didn't hear it," he said. "I am first to the dressing room. It's normal. If they are not happy, they can do this.
"I can only say good things about the fans. They are clever fans; we have a mid-table budget and we are fighting for a high position. They are enjoying the way of the club."
Boro head coach Aitor Karanka expressed his delight with the strides his club are making since he took over, and believes progress is being made in all areas.
He said: "It's my first season in English football and I'm very happy because everything is new to me.
"The potential is such that we have to work together to do the best. We have a good attitude and will be working to improve the squad in time."
Karanka refused to single this out as one of Boro's best performances, saying: "We have played a lot of games in recent times and played well but haven't won.
"We created some good chances in the first half and didn't let Brighton play.
"We are playing in a very high tempo and deserved a slice of luck when Brighton missed their penalty."
This was Boro's 12th clean sheet in their last 19 games and Karanka felt his men were fully deserving of their first win in seven away games.
He said: "I am very happy that we won, playing against a very good team. We had a lot of the ball and we knew we needed to go for the game."