The Reds' three-match winning run in the league, which had raised slim hopes of sneaking into the Champions League, was brought to a shuddering halt with the 3-1 loss at St Mary's.
However, while the top four - now nine points away - is realistically out of reach Henderson believes seventh-placed Liverpool can still secure a place in European competition next season.
"It was a big disappointment against Southampton but Europe's not gone yet," he said. "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."