The pair had to be separated by Virgil van Dijk early in Thursday night's eventual Europa League win over Sparta Prague after the Saints had been awarded a penalty.
Tadic tried to wrestle the ball out of the arms of Austin before he was escorted away by van Dijk prior to the Saints striker converting from the spot in the 5th minute of their 3-0 victory.
Regarding the battle for spot-kick duties, Austin told BT Sport 2: "As a centre-forward I think I should take the penalties.
"I've come here full of confidence, even though I've not scored.
"I put the ball on the spot and luckily it gave us a 1-0 (lead).
"I think it was a bit silly from me and Dusan but I'll take the penalties in future."
Austin added a second with a neat header on 27 minutes before Jay Rodriguez wrapped it up in injury-time.