On Saturday Watford, under new coach Walter Mazzarri, recovered from 2-0 down to win 4-2 away to West Ham United, before Claudio Ranieri's Leicester City, last season's champions, went down 4-1 at Liverpool.
On Sunday Francesco Guidolin's Swansea City and Antonio Conte's Chelsea played out a 2-2 draw that was one of the most eventful matches of the season.
"It's the English league, every game is very, very tough," contest said after failing to win for the first time in his five competitive matches with the London club.
What he learnt, if he did not already know it, was that a team as dominant as Chelsea were for almost an hour, need to make more of 28 attempts on goal.
"It's very difficult to talk because we lost two points," the former Italian national coach told Sky Sports.
"When you have the opportunity to kill the game, you must kill the game. We have to learn that.
"We are disappointed because the performance was very good in terms of our intensity and because we played good football."
Conte's view of Swansea's hotly-disputed second goal was backed up by a furious Gary Cahill, whom television replays showed to have been fouled by Leroy Fern before the Dutchman was allowed to run on and score.
"You could be sat on the moon and see it is a clear foul," he said.
"He came through the back of me. It was clear as day and seeing it back has made me even more angry.
"That kills me and kills my team. We have dropped two points which is massive in this league."
It was a huge goal too for Swansea after two successive defeats, and Guidolin earned credit for switching away from his 3-5-1-1 system before halftime, as well as apologising to Welsh international Neil Taylor, who was annoyed at being taken off to facilitate the tactical change.
"After Chelsea's first goal I saw my team not playing well and decided to change something before the end of the first half," he said. "I am sorry for Neil Taylor, but I decided this way because we needed a reaction."
(Editing by Martyn Herman)
