The Blues lacked fluency in south London but were able to back up their Club World Cup success in Abu Dhabi last weekend with three more points in the Premier League thanks to Hakim Ziyech’s 89th-minute volley.
It was Lukaku’s anonymous display which made headlines with the forward having only seven touches at Selhurst Park, the fewest in a single top-flight game for a player who played 90 minutes since Opta started collecting data back in the 2003-04 season.
“I am not so sure if I have a good answer to your question. I don’t know what it says. It says he was obviously not involved and could not make a point. I am not sure if it says so much about us in general,” Tuchel replied when quizzed about his £97million striker.
“We look a bit drained, a bit exhausted, and you can see everybody tries hard. Everybody is looking for the flow where you try hard but nobody sees you are trying hard.
“We are looking for it but in this moment we struggle, which is not a bad thing because everybody wants to be part of it and everybody gives their best but we do struggle a bit. For that it is important to win and keep a clean sheet so we keep on going.”
After beating Palmeiras to become world champions, Chelsea had a full week to get ready for the trip across the capital but Tuchel pointed out preparation was far from normal.
Captain Cesar Azpilicueta and Callum Hudson-Odoi sustained injuries in training on Friday and it contributed towards a disjointed performance.
Tuchel added: “You have no idea how a week like this works because we come from a 30 degree temperature difference, we have six players who have a cold from the AC (air conditioning) on the plane, we have jet lag that the guys have, no players who slept well in Abu Dhabi because of the temperature and the time difference.
“If you think we have a normal week to prepare, I can tell you it is not like this.”
The end result was still Chelsea bringing their lengthy top-flight break to an end with a victory that made it back-to-back Premier League triumphs after a 2-0 success over Tottenham on January 23.
While Tuchel has conceded defeat in the title race, he is not ready to give up hope of pipping Liverpool to second spot with their fellow Carabao Cup finalists on 57 points and seven ahead of the third-placed Blues.
“Unfortunately we don’t play them anymore,” Tuchel said.
“They look strong, they got a huge player (Luis Diaz) in the winter to make their squad even stronger. It is how it is but we will not give in.
“I will not tell you today that it is impossible to catch them but no other way than to improve our game, improve our style and to win game after game and to win consecutive games.
“There is no need to look at Liverpool, Man City or look behind. We have enough to deal with and enough to improve.”
Opposite number Patrick Vieira cut a frustrated figure at full time after Palace switched off late on to allow Ziyech space at the back post where he volleyed home Marcos Alonso’s cross.
“It was frustrating to concede the goal like that at the end,” the Eagles boss admitted after a sixth league game without a win.
“We knew we needed to defend well as a team for 95 minutes and I think we did it quite well.
“It just shows the quality of the teams of Chelsea and how important it is to keep concentration higher for all the game but we didn’t. To get punished like this is hard for the players to take.”