The Reds' run of three straight wins, which had raised their hopes of securing European football for next season, was brought to an end at St Mary's.
"It was a big disappointment against Southampton but Europe's not gone yet," Henderson told the Chester Chronicle.
"We've still got eight games to play and that's a lot of points to play for. We've still got to play some of the teams above us so we have to keep going.
"We have to pick ourselves up from this and ensure we respond positively against Aston Villa after the international break."
Liverpool face Aston Villa on March 30.