Leonardo Ulloa's injury time goal propelled the Seagulls to a 2-1 win over Nottingham Forest - and into the top six on a day of high drama at the City Ground.
Brighton will now face Derby in the first leg of the semi-final on Thursday, looking to secure their place at Wembley. And Garcia says they will have extra motivation - having lost twice to Derby already this season.
"They have beaten us twice this season. But we will be ready this time, we will be prepared and we will look to beat them this time around," said the Brighton head coach, who credited his players for their never say die attitude.
"We knew that our players would never give up; that they would fight until the end and we got the goal we deserved.
"It is a special time to score, in injury time, but I was happy for the players and for the fans, because they deserved this.
"The players never gave up, which makes me so happy. Craig Mackail-Smith had been out injured for a long time, so it was great to see him involved in the goal, when he crossed for Ulloa.
"It is impossible to get into the play-offs if you are not a team, but we were a team on the pitch."
Garcia said that he had not kept track of Reading's progress against Burnley - with their draw allowing Brighton to move above them.
"I did not want to know anything, about what Reading were doing, but I had the feeling that it would be in our hands," he said.
"I am really pleased for the fans, because we had great travelling support. Since the first day I was here, we have played for the fans and making them happy makes me feel really good."
Forest caretaker boss Gary Brazil felt his side had done enough to deserve victory - but said that there had been too many afternoons like it for them this season.
"It was another game that we should have gone on and won," said Brazil. "I could point to Charlton, Millwall and today - all games we should have won, which would be an extra nine points.
"Where would we be with those nine points?
"The result was harsh in that for good periods of the game we were very good.
"We got our noses in front and could have got ourselves another goal before half time - but didn't. (In the) Second half we did not play as well. We did not keep the ball well enough.
"We did not hurt Brighton enough. We gave them the opportunity to get back in the game.
"The two goals we conceded were poor goals. We did not defend the cross at the end and Brighton nicked the win to get themselves in the play offs."