The win moved Southampton up to sixth, ahead of West Ham United on goal difference and a point behind Manchester United. The top four sides qualify for next season's Champions League with the fifth-place finishers entering the Europa League.
"If (leaders) Leicester (City) can win the title, then we can be fourth or fifth in the league," Koeman told the club's website (www.saintsfc.co.uk).
"If we get another opportunity to play in Europe, we would like to take it.
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"We are doing well. We had a difficult start to the season. We had a difficult period in December but we are back again, fighting for a high position in the table, what we want.
"That's our ambition, to finish the highest position possible."
(Reporting by Simon Jennings in Bengaluru)
