Goals from Gabriel Jesus, Martin Odegaard, Bukayo Saka and Albert Sambi Lokonga all struck for the Gunners at the Camping World Stadium.
With the likes of Cesar Azpilicueta, Hakim Ziyech and Timo Werner all reportedly looking for a way out of the club, Tuchel was not enthused with how his players approached the game.
The Blues have only added Raheem Sterling and Kalidou Koulibaly to their ranks this summer while Antonio Rudiger, Andreas Christensen and Romelu Lukaku have left.
Tuchel has recognised the need for further signings ahead of Chelsea's Premier League opener against Everton on August 6.
Speaking to reporters after the match, the German manager said: "I am far from relaxed. We were simply not good enough. We were simply not competitive."
"The worrying part is that the level of commitment physically and mentally for this match was far higher for Arsenal than for us."
"They played I think what is their strongest line-up and structure that you see now for several weeks. This was the line-up they will try to start for Premier League games.
"It was surely not our strongest line-up. This is a part of an explanation but only a little part and the other part is worrying.
"I cannot guarantee we will be ready in two weeks."
"I look at the last season and parts of the game where we struggled, parts of the season where we struggled, and then we got sanctioned and players left us and some players are trying to leave us, and this is where it is," he added.
"So we had an urgent appeal for quality players, a huge amount of quality players. We got two quality players but we are not competitive like this. Unfortunately you could see it today."
