Chelsea meets Palace in the last four of the competition at Wembley on Monday (AEST), but breakout star Gallagher will be merely a spectator.
The England international belongs to Chelsea but is yet to make a senior appearance for the club, instead establishing himself as a top Premier League midfielder for Palace this season.
Gallagher has scored eight goals and provided five assists in all competitions in 2021-2022, including two assists in four FA Cup matches prior to the semi-finals.
That sort of form shows why Chelsea could not accommodate Palace's request to allow him to play this weekend. The Blues have won both matches against Palace in his absence this season, extending a winning run in the fixture to nine games.
"I had the chance to speak to Conor and I could also see his frustration," Tuchel said ahead of the match. "We met some weeks ago, after the international break, by coincidence in a restaurant.
"We had a chat, and the subject came up. I apologised, because I know how competitive he is, and I like him a lot. I know his character very well, and it was a pleasure to have him here in pre-season.
"This is the way it is. We play to win the game. The rules were clear when we made the loan.
"I can totally understand Patrick Vieira and the disappointment of Conor, but these were the rules when we made the loan, and we don't want to suffer from our rules."
Chelsea must still take on an England international brought through its academy, however, with Marc Guehi a permanent Palace signing last year.
Guehi, like Gallagher, has impressed at Palace, while Tino Livramento has been one of Southampton's star performers this season, but Tuchel explained their sales could not be reassessed with hindsight.
"It's a decision we took together. We are happy about these decisions," he said. "We cannot go back and reflect, because at the point where we took the decision it was the right thing to do, given the circumstances.
"It's very individual decisions. For Tino Livramento, for example, we had a plan and we preferred a loan, but he saw his future to go, and the situation was then better to agree to the sale.
"For Marc, it is a fantastic development. It's very hard or maybe even impossible to say if we had kept him he would be better or worse or the same. Maybe he needed exactly that, maybe he needed a change of environment, maybe he needed a different club, maybe he needed a bigger role, more minutes to develop your full potential.
"It just tells you over and over again that if you trust younger players and if you have a role for them, they can on a very regular level match your expectations or even over-perform.
"It's nice to see there are so many Chelsea players out there in every league. We are very well aware of it, and it's also nice to play against them and see them develop."
Chelsea still has academy graduates in its first team, with Mason Mount leading the way in terms of goal involvements (25 – 11 goals, 14 assists) this term.
Ruben Loftus-Cheek (31), Reece James (30), Callum Hudson-Odoi (28) and Trevoh Chalobah (26) have each made more than 25 appearances for the Blues in 2021-2022.
"We will always use as many academy players as possible," Tuchel said.
"Like I said many times before, it makes the club very special and makes every team in the world very special if you have the mix between world-class players, between big personalities from abroad, from outside the club, with the academy boys.
"I think it's very important also with the academy boys to match the level, to realise the level of commitment, of professionalism of players who come from other clubs, who bring the best of their cultures.
"It's very, very important for our youngsters to accept that mix and accept that challenge. Then it can be very special. This is what makes teams special, that there are players from the academy."