The Lions, who had only taken one point from their opening four games, looked on course for victory when midfielder Martyn Woolford drove them ahead shortly after the break at the Amex Stadium.
But Alan Dunne, booked earlier for time wasting, received a second yellow card for a foul on substitute Andrea Orlandi before Argentinian striker Leonardo Ulloa rescued a point for the Seagulls a minute from time.
Spaniard Garcia was not happy with Brighton's first-half display and said: "In this league if you do this then it's difficult to win.
"It's not easy to win consecutive games at home, or consecutive matches, but in the second half we played better than Millwall and deserved to score."
Brighton have seven points from five games going into the international break and Garcia believes steady progress is being made.
He added: "If you don't win at home you are not happy, but we are improving.
"It will take time because the players are understanding the changes we are making.
"Now we have a period of time when we can hopefully get players fitter."
One Seagulls player struggling with fitness has been Kazenga LuaLua, but Garcia was encouraged with the way the former Newcastle winger responded after coming off the bench shortly after the break.
Garcia said: "LuaLua has not been 100 per cent fit because of his knee injury and that's why he hasn't played as much as he would have liked.
"What we have now is a chance to get players fit. Then we will pick the best 11."