Harry Kane appeared to send Spurs on their way at St Mary’s scoring his 200th career goal for club and country to make it 1-0 in favour of Tottenham.
But things turned on Spurs in the second half as two goals in five minutes saw Southampton rally for the three points.
Yan Valery scored to level the proceedings in the 76th minute before James Ward-Prowse delivered an exquisite free-kick goal five minutes later to condemn Tottenham to defeat.
The loss leaves Spurs on 61 points, and rather than chasing a Premier League title, they could find themselves level on points with Manchester United after the weekend if the Red Devils defeat Arsenal on Sunday.
And Pochettino, who was forced to watch from the stands serving the first of his two-game touchline ban, was critical in his assessment of his team, noting that a top-four battle is their “real level.”
“I think it’s good now [that we’re in a battle for the top four] that people are going to realise our real level and stop with the perception,” Pochettino told reporters. “I am a little bit worried about the change from the first half to the second, it is mental. It’s about arrogance in a bad way.”
The manager took particular issue with the way his team started the second half after a strong first 45, which he believes let Southampton grow into the game.
That consistency is a large part of what he thinks is keeping Tottenham from joining Europe’s elite.
“It’s difficult to understand the second half, the way that we started the second half and the way that we gave the belief to Southampton,” Pochettino added. “I feel so disappointed.
“It’s too difficult in this level of competition like the Premier League when you are much, much better than your opponent and after 45 minutes you create a lot of chances and you dominate the game, I don’t understand why we change in the way that we change.
“Of course it’s too difficult to accept that. It’s a thing that worried me.
“It shows we need more. We need to increase everything if we want to arrive as one of the best clubs in Europe.
“There’s been a lot of talk about being in the last step, winning some trophies. We live in the perception and reality. This is the reality. We have two faces.”
Pochettino added that his squad needs to absorb the lessons that can be taken from this defeat and their recent struggles, which has seen their cushion in the top four race nearly disappear.
"This is our reality,” Pochettino told BBC Sport . “People talk about perceptions but we need to realise if you do not fight with intensity for the Champions League, you will struggle.
“The reality is you cannot only play for 45 minutes. We are a Champions League team, into the quarter-finals.
“The team does not have the experience of competing in these circumstance, it is good to learn but we have to fight every single opponent.
"We are fighting against big sides (for the top four). We had a big gap, welcome to the reality, we are under pressure to win games. It is a massive challenge for us."