Burley appealed for calm and an all-out effort against a Sheffield United team also struggling to kickstart their season, with the St. Mary's side coming from behind to snatch the points as the Blades were booed off at the final whistle.
Leading scorer James Beattie carved out United's opener in the 12th minute as the big striker put loan signing Christian Dailly under pressure.
The West Ham centre-back failed to clear as Keith Gillespie struck a sweet right-foot shot from 16 yards as he slotted the ball beyond Kelvin Davis into the far corner.
Southampton pulled level eight minutes later after trickery from Bradley Wright-Phillips, the little midfielder playing a reverse pass to Rasiak, who darted past his marker to finish, clinically drilling the pall into the net from ten yards.
The Poland international almost had a second as Andrew Surman picked out Wright-Phillips, his cross evaded the United back four as Rasiak stretched but just failed to connect.
United's creaky defence blundered in the 31st minute as the Saints snatched the lead. Surman's free-kick should have been cleared, but centre-back Chris Morgan and Paddy Kenny both went for the ball as Rasiak challenged, it fell at the feet of Viafara, who finished with a low strike from 15 yards out.
The Sheffield side were fortunate after an inch-perfect cross from Phil Ifil found Rasiak, he connected at the far post, but his header hit centre-back Gary Cahill and the ball bounced clear with Kenny flat-footed.