Ronald Koeman’s side earned a Europa League berth after finishing seventh last term, and an unbeaten run of six games has propelled them into contention for qualification again this time around.
Reflecting on the side’s current position, Targett, who started in Saturday’s 1-0 win away to Swansea City, said: "We weren't happy with the start of our season. We lost too many games and what we achieved last season I think we can achieve it again. We're in a position where we can do that, so we just have to keep looking forward.
"We had a little discussion. We're right where we want to be at this point, so hopefully we can get back in Euorpa again – that's our target for this season.”
Saints kept a sixth successive clean sheet when they blanked the Swans at the Liberty Stadium, and Targett, who played as a left wing-back after returning from injury, explained how comfortable the players feel in the 3-5-2 formation they used again this weekend.
"We've changed our system to play three centre-backs and two wing-backs and, at the moment, it's working very well. Teams are struggling to break us down, so it's going good,” he said.
"I think last season we were successful for all the clean sheets we kept, and some games Fraser's done so well for us, like the Arsenal game, making some world-class saves.”
Saints now have a weekend off coming up, before focus then switches to a home contest with an improving Chelsea side.
“We're all going to rest up and we know when we get back we're going to have to train hard, because Chelsea are a different team now and they will be a tough test for us,” said Targett.