The Rams brushed aside Garcia's men with a 4-1 victory on Sunday, a defeat that condemns the Seagulls to another season in the second tier.
Following a disappointing performance at the iPro Stadium, Garcia admitted he had no complaints over the result.
"They were much better than us, they deserved the win," he told Sky Sports.
"We had a lot of injuries, we've been trying to manage that from the start of the season and that's one of the reasons why I couldn't be prouder of the players.
"We played the most important game of the season with four of five under 21s. If we see the whole picture - it's been a very good season for us."
Garcia believes their 2-1 defeat in the first leg left them with an uphill battle, whilst admitting that his attempts to attack Derby backfired.
"We wanted to give everything, we wanted to gamble but it didn't pay off," he added. "In the first leg we were much better but they are extremely good in front of goal. Today we didn't play well and they deserved to win and go through.
"In the first leg I think we deserved much more but, to be honest, they are better than us and they showed that today."
With Brighton set for another promotion push next season, the Spaniard refused to comment on potential incomings at the AMEX Stadium, saying: "It's a question for the club and not me."