Clues to the answer could come as early as Wednesday with a trip to Arsenal in the Premier League.
"There is no time to be any more disappointed about one result," Saints boss Ronald Koeman told reporters on Monday. "It was three points, and Wednesday is another one.
"It is the best way to have a good reaction. Train hard, work hard and show it on the pitch - we have the chance this Wednesday."
Fans, commentators and critics alike broadly agree Koeman's side are playing some of the country's best football down on the south coast.
This term they have smashed eight goals past hapless Sunderland and remain the meanest defence in the top flight despite shipping three against the champions.
Even their most ardent supporters had long known, however, that their lofty position was due in no small part to an accommodating run of early fixtures.
The Arsenal game comes at the start of a six-week run in which Saints play both the Gunners and Manchester United twice as well as leaders Chelsea.
Burnley, Everton and Crystal Palace may offer some relative relief in that period, but these six weeks will provide the first real test of Southampton's European ambitions.
It speaks volumes for Koeman, the staff at St Mary's and Southampton's players that European football is even a topic of conversation after a summer of high-profile departures that had the Saints' installed as bookmakers' favourites for the drop.
Sitting third, with 26 points from 13 games, how Southampton respond to what was a first home defeat will offer an insight into their ambitions.
Skipper Jose Fonte insists Arsenal are now in the cross-hairs as the Saints looks to bounce back immediately.
"We have to. There's no time to think about negatives and losing. There's no time. This is football," he told reporters.
"Sometimes you win, sometimes you lose. We lost against the champions. Obviously, we are not happy but there's no time to think about what-ifs or stuff like that – it's just focus on the next one."
Southampton will be without French international playmaker Morgan Schneiderlin who is out with a thigh injury.
(Editing by Ed Osmond)
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