Pochettino and Chelsea have parted ways in the last 24 hours after he guided the club to sixth place and Europa League qualification.
Melchiot told BBC Sport: "Mauricio Pochettino came in and it was very difficult for him. It would be difficult for everybody. But then he managed towards the end.
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"People always say that the end of the season sets you up for the season that's coming. Maybe not all the games he was convincingly winning, but he built the team and got them into a European spot.
"And that is the thing, exactly what I said at the beginning of the season. Europe should be that focus, nothing else.
"Don't ask for a championship, don't ask for trying to go for the title or try to make it to Champions League because that was a big jump. But getting into Europe, come on guys. That should be something for you to consider (giving) him one more year."