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Well, Chelsea needs to wait and trust the process as they have no other options or alternatives. In the chelsea squad there are average defenders and poor strikers; 0 goalscorers at all and injured creative midfielders. No manager will succeed in such circumstances, and sacking and employing new managers without getting a striker will only push Chelsea project into more terrible circumstances.
The Chelsea team is bad and not good enough; the earlier supporters accepts this, the lower the expectations too.
Chelsea don't need to fire Pochettino after just 6 games, but they need to push him to get his team better. I don't think Pochettino managed to make the team's dressing room any more lively regardless of the outcome of the match, but tensions became more likely. Pochettino has to start from small things and improve them, that includes improving the atmosphere in his team's dressing room for the better.
Liverpool also have many players whose quality is almost the same as that of Chelsea, but Klopp is here to improve it and get his players into the best shape. He turned his team into a competitive team even though Klopp has not won as many titles as Manchester City. Pochettino must learn from Klopp and Arteta instead of being a coach who tends to stay silent on the sidelines.