Nathan Jones was in the stands as he watched his team beat Wednesday on penalties.
St Mary's is expected to have a new manager soon.
Josh Windass gave League One Wednesday the lead, before James Ward-Prowse equalized from the penalty spot.
Dominic Iorfa's saved spot- kick meant the Saints progressed.
It was a run of just one win in nine games that led to the dismissal of Hasenhuttl.
The Saints replaced him with Jones, who led them to the Championship play-offs last season.
It looked as though they would be on the wrong side of an upset when Windass drove in the opener midway through the first half.
The home side took control, though, with James Ward-Prowse converting a penalty on the stroke of half-time before Theo Walcott had two efforts cleared off the line.
Walcott scored the winning goal and Alex McCarthy saved Iorfa's spot- kick to send the home side through.
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