Mark Hughes's men struggled last term before narrowly avoiding relegation and there was little in their performance to suggest they will be much better this term, as Burnley, which was in UEFA Europa League action in Istanbul last week, secured a point.
Burnley was easily the better of the two teams in the first period, with Saints goalkeeper Alex McCarthy making several stops to keep the hosts level.
Southampton did look more threatening in the second half and troubled Joe Hart a few times late on, but its efforts were not enough to break the deadlock.
In a first half that generally lacked quality, Burnley looked the more likely to score, starting well and going close through a Chris Wood header, before Jack Cork saw a goal disallowed for straying offside.
McCarthy then had to be alert to deny Aaron Lennon from close range, rushing out to block the winger's effort 11 minutes in.
Saints gradually improved as the half progressed, but they were lucky to go into the break level, McCarthy producing a smart save from James Tarkowski after Ben Mee's overhead kick fell kindly to him at the back post.
Burnley initially took control again in the second half, but had a lucky escape just after the hour, Ashley Westwood clearing off the line when Mee looked destined to score an own goal.
Hart then did well to keep Dale Stephens at bay 18 minutes from time, before Mario Lemina went close with another header, but otherwise Burnley looked good value to at least leave with a point.
The Saints' first away trip of season sees them travel to Goodison Park to face Everton next weekend, while Burnley will host Watford a day later after Friday's (NZST) UEFA Europa League qualifier against Istanbul Basaksehir.