The 24-year-old faces a six-month spell on the sidelines after sustaining a ruptured anterior cruciate ligament in last weekend's 4-1 Premier League defeat at Manchester City.
The former Burnley frontman is now out of contention for England's FIFA World Cup squad and will miss the start of next season as he prepares to undergo surgery.
Pochettino has been impressed with the attitude of Rodriguez, who scored 15 goals in 33 top-flight appearances this term, and expects him to kick on when he returns later in the year.
"We're all very sad for Jay, but we know he's a very strong character. He's an optimist and he's doing well mentally," Pochettino said.
"I am certain that Jay will become stronger from this situation. I'm positive that he'll return reinvigorated.
"Jay has been coming to the training ground every day, and he's started his recovery already. He's in high spirits.
"At the moment, the medical team is working to bring Jay's swelling down and then will decide when is best for his surgery."
Rodriguez's absence is a bitter blow to what has been an impressive Southampton campaign, as they occupy eighth place with 48 points ahead of Saturday's visit of struggling Cardiff City.
Pochettino is determined to finish the season on a high note and better the south-coast club's record Premier League points tally of 54.
"There are still five games left in the season. We're all professional so we're focused on finishing the job as best possible," he added.
"(On Saturday) we'll have to work our socks off and suffer against a team that are fighting to stay in the Premier League.
"We have to defend our shirt in every single game – that's always our motivation.
"After Jay’s injury, tomorrow is a very good chance to show our strength as a team.
"We're aiming for the maximum points we've ever had in a Premier League season – that's a massive motivation for the players."
