Saints boss Ronald Koeman will be disappointed his side only left Goodison Park with a point as both Shane Long and Dusan Tadic hit the woodwork when the game was tied at 0-0.
Everton, however, took the lead against the run of play as Argentine centre-half Ramiro Funes Mori's deflected shot found the net after some sloppy Saints defending,
Sadio Mane quickly equalised for Southampton to create a frantic finish to proceedings. However, Southampton couldn't find another goal against an Everton side left on the ropes.
This was a big opportunity for Southampton to state their claim for a Europa League spot but this was not the result expected against an inconsistent, out of form Everton side.
Southampton spent more than twice as long as the Toffees in the opposition third but failed to capitalise on their pressure to win away at Everton in the league for the first time since 1997.
Southampton have now gone eight games without a clean sheet following a run of six consecutive games without conceding.