The England international was in fine form as Everton lost 2-0 at St Mary's Stadium on Saturday - the result sealed by own goals from Antolin Alcaraz and Seamus Coleman.
Southampton's captain has been tipped to star for his country at the FIFA World Cup, although his consistent performances have also attracted attention from Southampton's Premier League rivals.
Manchester United have persistently been linked with a swoop for Lallana as well as Southampton's teenage left-back Luke Shaw.
Les Reed, executive director at St Mary's, insisted on Friday that the club will not be forced to sell any of their leading players, but Lallana is remaining coy on where his future could lie come the end of the season.
"I just want to enjoy my football," he told BT Sport. "That's when I'm at my happiest, when I'm playing well.
"Playing in a great, youthful team like this I feel like one of the experienced players nowadays.
"I just want to concentrate on the last two games of the season and we'll sit down in the summer and see what happens."
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