Garcia, who took over from Gus Poyet after a turbulent Summer at the Amex Stadium, added what makes the start even more disappointing is the fact that the Seagulls have thrown away leads in each of the matches.
The start of the Spaniard's tenure has been badly affected by injuries and he is keen to strengthen the squad, having recently swooped to add Bolton midfielder Keith Andrews on a season-long long.
Derby clinched victory before a crowd of 26,238 at the Amex with striker Chris Martin's brace following Leonardo Ulloa's opening goal for the Seagulls, and Garcia said: "It was like the other games.
"We had chances to score but were not clinical, whereas Derby took their chances. We've had the lead in all three of our games so far and have ended up losing.
"If I had a dream this would not be the start I would have wanted. But we have many, many games to play and we will improve."
Garcia, who is having to do without injured midfielders Liam Bridcutt and Andrea Orlandi, is keen to put his own stamp on the team by making some changes.
He added: "I need to change some things because every manager wants to introduce different kind of things.
"After we conceded the second goal we played as I want us to play and we will improve. Obviously we are hoping for a bit of luck as well."
Derby boss Nigel Clough is tipping former Norwich striker Martin to play a major role in his side's challenge for the play-offs.
Martin was with the Rams on loan last season and moved on a free transfer.
An enthused Clough said: "He is the one that we are most pleased with.
"It's very important for him to get a few goals as he is our main target man. He did well while on loan and needs a home with us. Hopefully he'll stay with us a few years and help us achieve what we want to achieve."
Clough also insists there is "nothing wrong" with aiming high and says his men are striving for the top six after several mid-table finishes.
He added: "We believe we are as good as anyone in the league. We have got to get confidence through to our young side to help with the belief that we are as good as other teams."
Clough was especially delighted to achieve a win in his side's first away league game, as the Rams only won four matches on their travels during the whole of last season.
He said: "There was a bit of everything in our performance. The way we started pleased me the most and we controlled the game for long spells.
"We didn't deserve to go behind and once we had taken the lead we had some good situations ourselves."