But their strong start shows no sign of slowing, and the Kenyan midfield enforcer is right to be aiming high given the situation Saints find themselves in.
Simply put, they're an excellent side with an excellent manager in a very enviable financial position.
Sacking Nigel Adkins after an unbeaten run and 2-2 draw at Stamford Bridge enraged fans and neutrals alike, but ruthless chairman Nicola Cortese is yet to make a bad decision when the pressure is on and was soon vindicated in his appointment of Mauricio Pochettino.
The new man's C.V. hardly inspired confidence within the fanbase; His 49 wins in 146 league matches with previous club Espanyol was questionable to say the least, and he'd been sacked with the Barcelona-based team rock-bottom of La Liga.
But it wasn't long—12 days, in fact—before Pochettino's Saints were drawing praise from all corners, with Sir Alex Ferguson admitting to BBC Sport that his Manchester United team were lucky to beat Southampton at Old Trafford.
It's not every day you hear that.
The team ensured they were safe from relegation weeks early and sputtered over the finish line and have picked themselves up accordingly to start the 2013-14 season in imperious form.
The Saints sit fourth in the Premier League table going into the international break, having accrued 14 points and conceding just two goals. They're only below Chelsea on goal difference and have kept five clean sheets in seven outings.
What on earth has gone so right for the South Coast club?
It starts with Pochettino getting the best out of the players he inherited—a talented bunch, make no mistake—and really getting to know them in the half season he managed them up to the summer transfer window.
He thrust a 17-year-old Luke Shaw in at left-back on a permanent basis, built a relationship between Jay Rodriguez and Rickie Lambert and dropped the underperforming Gaston Ramirez.
This summer only three players were purchased, but each were excellent or world-class additions in their own right.
Pochettino derives from an astute tactical tree of knowledge, aligning himself with the likes of Marcelo Bielsa and Gerardo Martino, and preaches high-pressing, possession football wherever possible.
The changes have been both subtle and obvious: He moulded Morgan Schneiderlin into an interception machine and has since placed Wanyama alongside him; Dejan Lovren has come in to lead the defence and make Jose Fonte twice the player he was last season; Daniel Osvaldo's presence has changed Lambert's role and made the side less reliant on the big man up front.
Southampton are switching formations mid-game for fun, with each and every player tactically drilled in what they are doing. One minute it's a 4-2-3-1, the next it's a 4-4-2: the movement has been tough for every opponent to deal with so far.
Shaw, at left-back, is sensible enough to tuck in when Nathaniel Clyne bombs forward on the right, effectively giving Pochettino a platform of three to defend counters with Wanyama just ahead.
Incredible faith in the South Coast club's academy has been extended to James Ward-Prowse and Calum Chambers, both 18 years of age, and JWP in particular appears one of England's brightest prospects in midfield.
"Poch" has shown no reservations in moving players around, and while the veteran likes of Steven Davis enjoy the variety, the younger players are subjected to it too: JWP has appeared on the right wing this season in order to cross for Lambert and protect Chambers from double teams.
When you have a smart manager, things fall into place. When that manager is backed by a considerable fortune, things fall into place extremely quickly.
Pochettino's astute approach, willingness to give youth a chance and excellent eye for a transfer has allowed Saints to make gargantuan strides in the Premier League, and it's easy to see why they're occupying fourth right now.
That won't last, but original predictions of them finishing around ninth now look harsh; this side has the talent and depth to challenge for European spots in a rigorous, long, demanding season.
If Pochettino can rebuild his bridges with a disillusioned Jack Cork and find suitable left-back insurance for Shaw, this team has an extremely high ceiling.
It's not a phase, it's not "just a good start"—the Saints are marching on in undeniably impressive fashion.