The 1-0 win away to Swansea last Saturday saw Ronald Koeman’s side extend their unbeaten run to half-a-dozen games and climb up another position in the standings.
Midfielder Clasie wants to make sure the team finish in at least sixth place, while he remains optimistic they could yet improve on that.
“Now we are sixth, but we're looking forward to the fifth position. We're one point behind Manchester United.
“But I think the most important thing is to look to yourself and win your home games and take your points and then we will see at the end of the season where we are.”
Clasie, who has been an integral part of Saints’ recent run, said the trust among the group has been one of the key factors in their run of good form over the last six games – none of which they have conceded in.
"I think the last few weeks we've got a lot of confidence,” said the Dutch international. “That's normal when you win games. You play good, take your points and you get a lot of confidence.
“It's important for us we trust each other and we are doing very well the last few weeks and hopefully we can go forward to this kind of things in the games.
"You have to work every week hard to take your points. It's the Premier League, every game is difficult and we know that.
“But the confidence and the trust in each other is so important for a team, and then you start in the game with defensive organisation, and I think in the last few weeks that was perfect.”