The Argentine indicated he has "maximum respect' for the ex-Saints manager after replacing him at St Mary's, while Adkins was defiant and is looking forward to a "great challenge"
The Saints claimed their third league win in a row at the Madejski Stadium, with Jay Rodriguez and Adam Lallana scoring in each half.
The win improves the south-coast outfit's record against lower-half clubs, but they were noticeably slower out of the blocks than in the wins over the likes of Manchester City and Chelsea, something the Argentine hinted was due to the Royals' long-ball tactics.
"We have to analyse the game and rival we're facing," he told reporters. "When facing a rival who's just kicking the ball in the air there's no point in pressing really high. The ball is always in the air so there's no point.
"Our tactic is to pressure and play from the back, but we don't have just one tactic. We try to give our team the capacity to deal with different situations in different ways, but we try to maintain our philosophy, attacking football and high pressing."
The win leaves Saints with 37 points and virtually secures their Premier League status for another season, however the 41-year-old is still focusing on one game at a time.
"Today we played a good game, but there are still a lot of points to be won," he continued. "Our goal is just the next game against West Ham."
The former Espanyol manager was facing the man who he replaced at St Mary's - Nigel Adkins - but once again insisted there are no hard feelings between the pair.
"I have maximum respect for Adkins in a personal and professional manner," he added. "I wish him all the luck in this new job at Reading. I am pleased however of the performance of my team.
"I thank Nicola Cortese for the possibility of being here. I think players belong to the club and there are a lot of people working behind the scenes that made Southampton what it is today.
"Yes of course [I'll accept his invitation of a drink] . It's a tradition in England which I really admire and appreciate."
Adkins, who was in charge of his first clash at the Madejski, mirrored Pochettino's views before insisting he is relishing the challenge of keeping his new club the Royals in the Premier League.
"[The] clubs were first and second in Championship last year," he said. "Southampton are going to stay in the Premier League next season and we've got a challenge on our hands to achieve that.
"It's a great challenge. Someones got to go and do it, and I'm pleased to be doing it. If you look at the players effort, especially in the firs half, it shows they're committed to having a go. And we've got to keep building on that.
"Maybe the best thing to do is not even look at the league table. Their professional players, what they've got to do is work hard on the training ground in preparation for the next game."