Pochettino's side have won just one of their last eight home league games but have picked up points against high-flyers Manchester City and Arsenal in that time.
Victory at St Mary's Stadium against Norwich City on Saturday could move them back up to eighth if Newcastle United fail to beat Fulham.
Pochettino is eager to turn draws into wins on home turf and finish in the top eight come the end of his first full season in charge of the club.
"This club is having a historic season with the number of away wins we've had, but we could've done better in some home games," he said.
"We want to continue playing well and to change the dynamic of the results we're getting at home.
"We're ninth in the table, but we want to be eighth and to keep climbing. Tomorrow we have an opportunity to do that.
"Tomorrow's game will be very difficult. I think it’ll be similar to last week's against Crystal Palace. That was a good lesson for us."
The club confirmed the appointment of Ralph Krueger as chairman earlier this week after the departure of Nicola Cortese in January.
Pochettino is hopeful the club can enjoy stability under the guidance of Krueger, who has never held a role in football before.
"It's clear that this club needs tranquility after the upheaval of January. We need to move forward in a calm and relaxed manner," he added.
"When I spoke to (owner) Katharina Liebherr for five minutes before my press conference in January, she told me that she wouldn't sell the club.
"From my point of view, the speculation ended in mid-January when Katharina told me there was no intention to sell the club."
Pochettino also confirmed midfielder Victor Wanyama is doubtful for Saturday's game after "falling back into the injury (leg) he had three months ago" in midweek, while Jack Cork is set for a spell on the sidelines with an ankle injury.
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