Jürgen Klopp's side head to St Mary's today for their second Premier League fixture of the season after returning home from Istanbul on Thursday.
The showpiece at Besiktas Park in midweek involved extra-time and penalties following a hard-fought 2-2 draw, although Adrian believes the fact the Reds emerged victors should ensure they head to Southampton with a spring in their step.
"When you win you have a positive mind and the recovery is quickest and your body feels much better," the goalkeeper told Liverpoolfc.