Its not really bad with Chelsea victory from Brighton Albion in EFL Cup have opportunity for Pochettino get one trophy in the end of season looking realistic with consistent performance in Premier League, I don't think any special performance or achievement success become the winner of EFL Cup than finish on top fourth standings place have Champion League spot position. Not really important with how far Chelsea lead in EFL Cup if got bad performance in Premier League he will get warning or potential sack early before end this season.
I agree with you, An EFL Cup win without top 4 is a waste of performance and efforts; and it would mean the season didn't get desired results or target as the board would have mandated before the start of the season. Also Chelsea have gotten 2 back to back wins in the EFL, Which means they are lacking an edge in the Premier League.
Pochetino needs to make his team to find their feet in the premier league because their next 10 games are huge ties; they fumble half of those ties and Chelsea can be battling relegation by Christmas. Big performance needed