It leaves Brighton and Everton on eight points from eight matches. Chris Hughton's newly-promoted side will take that return but it is not good enough for their opponents.
The result leaves Everton in 16th place, with Brighton two above on goal difference. An even more damning statistic is that the last away league win for Koeman's side was back on January 21 at Crystal Palace.
In a sense, Wayne Rooney sums them up. The 31-year-old was used as a central striker and struggled.
He appeared off the pace and out of touch and, in the second half, complained vehemently that he was fouled when all that happened was he sloppily lost possession. Yet, he had the coolness to roll the ball into the net to salvage a point with his last touch before he was substituted.
That goal also meant only Frank Lampard (39), Andy Cole (38) and Alan Shearer (37) have scored against more different clubs in the Premier League than Rooney, now on 36.
There was little difference between the sides. Brighton's defence is rock solid, though, with Dunk and Shane Duffy, and record-signing Jose Izquierdo certainly made a difference when he came on as a substitute.
Knockaert went agonisingly close as his goal-bound shot struck Keane, but the Frenchman made the breakthrough, the ball squirting to him off a rebound.
Everton almost snatched it at the end through substitute Kevin Mirallas only for goalkeeper Mathew Ryan to make a superb double-save. That would have been hard on Brighton and relief for Koeman. Instead, it finished in an unsatisfactory draw.