Defenders Antolin Alcaraz and Seamus Coleman scored own-goals in the first half at St Mary's on Saturday to dent Everton's UEFA Champions League hopes and move eighth-placed Southampton on to 52 points - which was their final total in the 2002-03 top-flight season during Gordon Strachan's reign.
The south-coast club reached the landmark with two games remaining, against Swansea City and Manchester United, and a delighted Pochettino hailed his side's exploits, before challenging them to break new ground.
He said: "I thought overall we need to congratulate the players and all the staff involved with Southampton.
"Today we have equalled the maximum number of points that this club has ever achieved in the Premier League.
"That takes an amazing achievement. That's what we've done today and I'm just really happy for the players and everyone involved with this club.
"But it's also true that we have two more games. Why not try to get two more victories out of these two games? That's what we want to do.
"In the overall analysis of the season, we're having a fantastic season and we're very pleased with how the season has gone."
Pochettino was in no doubt that his side were worthy winners against Roberto Martinez's fifth-placed outfit.
"I think we created the chances to make those own-goals happen," he added.
"Overall we had a great game. I want to congratulate the players because they had an amazing game against a team that is trying to break into the Champions League and trying to break into the top four."
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