The Argentine manager was booked after striding onto the pitch and confronting the referee.
Asked about the incident, Pochettino apologised after confronting the Anthony Taylor-led refereeing team: “I need to apologise to Anthony and the referees and the fourth official.
"In this moment, I feel that maybe Raheem [Sterling] can go through and go to score the fifth and in this moment when the game finishes I turn and say “what the ….?” You know, what’s going on.
"I said 'why stop in this moment, the action.' Then I turned and said 'I deserve, I deserve to be booked.
"Because I crossed the limit, so I want to apologise because it’s not a good image for me and for football, this type of behaviour.”
There were nine yellow cards at Stamford Bridge in a heated match in which Chelsea had to come from behind three times to earn a point.
Chelsea dealt well with disappointment, especially after Rodri's deflected shot looked to have won the match in the 86th minute.
Pochettino was proud having seen arguably the best performance of his tenure against Pep Guardiola's treble winners.
"The players deserve full credit because the performance this evening was amazing," the Chelsea boss added. "We face a team that for me is the best team in the world.
"Too many circumstances that happen during the game that make me very prod because of the way in which we managed the game was really, really good.
"Of course always things to improve but it’s the process when you want to build a journey and want to build a project from zero.
"This type of thing are really good and this type of experience, games will improve a lot our players, our team but now we need to use and translate it in the future."