A convincing display from the playoff hopefuls against a team set for the Premier League next season means that Brighton are just two points outside of the top six with five games remaining in the campaign.
"This was a massive result for us and I could not be more proud of my players for the way they performed," Garcia told reporters.
"We have been playing pretty well and were wanting to win against a side going into the Premier League. We wanted to come here and play well but we knew it would not be easy against the a team like Leicester.
"The win has put us in a good position but I only look at the next game and focus on that. I hope the players do the same."
Brighton host Charlton Athletic in their next match on Saturday afternoon.