"The race for a top four finish will go down to the wire and if we keep up the good form, playing in Europe's premier club competition could easily become reality," Tadic told Belgrade daily Sportski Zurnal.
"It will be tough because Manchester United and Arsenal are very good teams and will do everything they can to leapfrog us, but it's now down to us to repel their onslaught."
Sunday's win, courtesy of a goal by second-half substitute Tadic, lifted Southampton into third place on 39 points from 21 games, two ahead of United and three in front of Arsenal.
Asked whether the reason he took his shirt off and flexed his upper body muscles while celebrating the goal was to imitate Cristiano Ronaldo and Mario Balotelli, Tadic said: "No, I wanted to show Manchester United fans how strong I am and who's the boss at Old Trafford.
"I didn't really plan it or think about the way I would celebrate if I scored. It was a spur of the moment thing.
"I also want to thank our fans for their fantastic support, they were outnumbered by United supporters by 10 to one but were more vociferous and carried us throughout the match."
(Editing by Ossian Shine)
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