At least it has been an entertaining win for the fans who have pinned a lot of hope on Pochettino so far. Brighton is a good team to provide the best resistance against Chelsea, but Chelsea managed to overcome the challenge even though they could only score 1 goal.
I know this is an important win for Pochettino's squad, but they cannot be satisfied with just one win in 4 matches in two different competitions. Chelsea fans and management are hoping for more positive results rather than just 1 in 4 matches, so Pochettino clearly has work to think about ahead of the match against Fulham early next week.
You could say, the victory was an entertaining victory for the Blues fans, as you said. However, it is not the EFL Cup that is their target, Chelsea must be able to finish in the top four of the Premier League competition. thus, they can take part in the Champions League next season. However, the victory in the EFL Cup over Brighton could be a trigger to raise the motivation and mentality of the entire team to play their matches in the Premier League.
This week, they will play a match against Fulham. Pochettino must further improve the quality of his players' play, so that they are able to provide victory after victory to increase their ranking in the standings.
Now Cheslea is in 14th position, Pochettino has a tough task to bring Chelsea up the rankings. Luckily, the competition still has a lot of games left. Pochettino must optimize his squad, while waiting for the injured players to fully recover.