At a time when the club's situation has not improved after Roman Abramovich left, this season is the best achievement that has been achieved. The Blues have really been going through a period of transition for several seasons and new owner Todd Boehly has made a massive investment to revive the club's reputation so that it can be respected again. However, it was not easy for Boehly, he had to be patient to enjoy the results, but even though he succeeded in bringing Chelsea to finish in 6th place, in fact Pochettino was fired. As a result of this decision, I once again doubt Chelsea's existence next season because the players have to adapt again to their new manager and that will not be easy.
Chelsea's transitions in the most recent seasons has been a typical part of their instability all along, If they happen to get some form of balance both in their coach and in the management, it will be a leveling ground upon which they can kick off to start their journey to becoming stable again and probably been amongst to teams in the premier league as they should be but then they just sacked their coach.
With pochettino Chelsea was gradually getting to attain stability again which would have helped them well enough to be able to get back in their form as they should be but then sacking him at this point is really going to have a serious effect on them especially in the fact that they will have to start all over again getting to groom the team to adapting to the new manager and aswell his strategy with which he will be waiting the players to get on with so they will be able to get the best of the league in coming season, it may seem like a tough one but since the management has decided then they will have to work with it.
Some of the players who were already getting accustomed to the strategy of pochettino will have to start all over again which may have an effect on their mentality, they may aswell not be able to eventually attain that stability early enough again rather it may take them a whole lot of time this season, but then they are some of the players may be sold aswell probably by choice of the new coach and then new ones which he my recommend may be bought and are going to help them grow faster.