On-loan Chelsea striker Patrick Bamford settled the match with a superb finish 14 minutes from time, but McClaren was also delighted with the part his other replacements played in beating the team with the best defensive away record in the Sky Bet Championship.
Brighton had conceded only nine goals in their previous 12 away games, and a scrappy contest littered with niggling fouls appeared to be heading for stalemate until Bamford pounced on his home debut.
The first half was largely forgettable apart from a superb save from Lee Grant, who reacted brilliantly to tip over a bullet header by Matthew Upson from a Andrea Orlandi corner in 26th minute.
Derby had been frustrated by a well-drilled Brighton side, but the visitors could nothing to deny Bamford when he placed a precision left-foot shot inside a post following a one-two with Jamie Ward in the 76th minute.
McClaren said: "Patrick showed great composure. There was no panic. We know he's got that quality and it needed a calm head in that situation.
"It's great when you have players who can change a game. It's not about 11 players - it's the squad, and we had 14 players who contributed to that win. In the modern game, it's absolutely vital because the game was going nowhere and we knew that at half-time.
"Jeff Hendrick came on, started in midfield and then went to right-back, which allowed Conor Sammon to come on so we could go to 4-2-4 and try and win the game, and Patrick produced that moment of quality to win it.
"It's a squad game. You need players who can come on and help change a game, and the squad won that game today, not the team."
Brighton manager Oscar Garcia revealed he had left unsettled midfielder Liam Bridcutt behind because the player was not in the right state of mind to play.
Bridcutt recently handed in a transfer request and Garcia said: "He said yesterday (Friday) he wasn't focused on the game 100 per cent. He was honest with us and, because of this, he didn't come with us.
"I had picked him to play today but he wasn't focused and in the next week, if nothing happens, I have to ask again. It's a problem between him and the club and they have to solve it as soon as possible.
"The best solution is as soon as possible because it would be better for the team, but these things happen in the transfer window.
"But I am not worried because the other players are fit enough and want to give 100 per cent for me and the club and I was proud of their performance today."
Brighton missed out on striker Lewis Grabban, who decided to stay with Bournemouth, but Garcia added: "We are looking to strengthen the squad and the club is working on a list of targets."