Chelsea were without Romelu Lukaku, Timo Werner and Callum Hudson-Odoi due to positive Covid-19 tests, with Kai Havertz ill and another possible coronavirus case.
Yet Everton were even more badly impacted, with Rafael Benitez fielding a much-changed team as his side battled to a cling on to a valuable point.
Jarrad Branthwaite poked home Anthony Gordon’s free-kick to stun an otherwise-dominant but highly profligate Chelsea, who had moved ahead through Mason Mount.
"Obviously it is difficult to get points here but the way we did it with so many senior players not available and players on the bench still with some issues, the young players, the way they are working," said Benitez.
"They did everything they can do to get the points. Sometimes you need a bit of luck, this year we are not very lucky with all the injuries.
"The fans have been great from day one, the reality is since the first day against Southampton they have been fanatastic and you could see today they were enjoying it.
"The game plan was the same, we had two or three days to think about how to play against them, after we have to mix the players and see who is available. Without practicing too much they knew exactly what we were looking for."
Chelsea spurned a glut of gilt-edged opportunities to slip four points behind leaders Manchester City in the Premier League title race, and have now picked up just 12 points in seven top-flight matches.
Chelsea are still slated to face Wolves at Molineux on Sunday despite football matches falling foul of Covid cases up and down the country, leaving Tuchel determined to plot a route back to form for the stuttering Blues.
Asked if Chelsea find themselves in a blip or a rut, Tuchel replied: 'I would be more concerned if we were totally out of form and always conceding the first goal and struggling to come back.
"Maybe that would be easier to analyse; I don’t think it’s so easy to analyse our situation.
"I saw teams struggle at West Ham, but for us all our huge problems came more or less out of nothing, for all three goals.
"I can go on: against Leeds we were under control, a good first half, then we score, and then the game gets out of our hands.
"Today, please: it’s a freak result for this kind of match. So where to point the finger and where to start?
"There are some facts that we concede too many goals, that we give away too many leading positions, this is a part of that. But we are very honest and very critical. But for me, it’s not so easy to analyse why we’re dropping points.
"It was the same against Burnley at home, the investment we put in for getting goals is so huge.
"I can never say we don’t play with full effort, discipline and ambition, but it slips and we get punished for not getting a lot wrong. It’s a bit awkward and strange to analyse.
"We could be sat here talking about a 3-0 win that would be fantastic because of the players we missed, but again it is mistakes that has cost us."
Asked if Chelsea had wanted the game postponed due to the Covid cases, Tuchel added: "No we did not discuss one second about it.
"I don’t even know the rules and am not interested in knowing them, I just prepare my team. We knew at 12 who was ready to play and who was out.
"And the focus is always for the guys who play. Whether the game gets called off or not is none of my business."