The saints fans really don't like Pellegrino. They want him out already.
To be fair, I never understood the idea that Pellegrino was going to be the anti-Puel. You only needed to look at how Alaves played last season to see they were both pretty similar. Safety first, low-risk style of play. Puel was sacked mainly because fans a) thought the style was boring and b) because the gap between them and the European berths had become extended so dramatically. Like a lot of teams their season tanked in late December/early January. It probably wasn't helped by the fact Van Dijk was injured, Fonte wanted out and they didn't bother to sign any forwards until January, despite selling Mane and Pelle in the summer window. He still got them to a cup final. Yeah, they should have likely done better with in a EL group with Sparta Prague and Hapoel, but they still finished above Inter in that group.
Southampton should have taken £70m for Van Dijk: a player that had missed a ton of football and whose sale could have brought in 2-3 quality players. Instead they focused on principles, which while an honourable thing, might not count for as much if you end up slipping down the table and start panic buying in January. They've won four games in their last twenty going back to last season. And despite needing goals, Southampton have only signed one forward (Gabbiadini) in the last three windows, while relying on talented, but massively injury-prone forwards (Austin and the now departed Rodriguez) and making Shane Long, who should be at best a third-choice in a team of Southampton's purported ambitions, as their lead striker. Meanwhile they have at least six players who can play centre-back (Stephens, Van Dijk, Yoshida, Hoedt, Bednarek and Gardos) despite having no EL football.