The Blues were at their free flowing best in the contest on Monday night at Stamford Bridge.
Cole Palmer scored four goals, with the result looking beyond down mere 15 minutes into the game.
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(It will) be a long debrief that," Tarkowski said after the match.
Underperformed, the most embarrassed I have felt as an individual.
It shows where we are at today. We can only apologize to the fans who supported us. It is on the players, it is not on the manager and the staff.
No excuses on our behalf, we need to brush ourselves down as we have a big few weeks coming up.
We conceded six goals and you should feel embarrassed.
Nothing to do with technical aspects, people getting beat and run off and it is hard to summarize it. I have had dark times here but the fans stick by us in the next game so hopefully they'll be there for us again."