Needing a final day victory to ensure survival, the Bees were sunk by two second half goals from Roy O'Donovan and Luke Guttridge at Northampton, who now face Cheltenham in the play-offs.
The former Champions League winner, who played at some of Europe's leading clubs during an illustrious career, had turned the club's fortunes around since taking over as head coach. But it wasn't enough in the end as AFC Wimbledon beat Fleetwood 2-1 to climb out of the relegation zone at Barnet's expense.
The former Dutch international said: "It's a bitter pill to swallow and the players are very disappointed but they gave it everything. It wasn't all down to this last game, we had a lot of opportunities during the season but didn't take them.
"It's even more disappointing because we have reached all the objectives that the chairman set and reached the 51 points target but we've still gone down.
"The players can look themselves in the eye and know they have given it everything they had. But you have to be sharp enough to take the chances you create especially against a team like Northampton. They were clinical in the second half.
"Losing a Champions League final was a bad experience for me but I'm aware of the consequences for the club going out of the Football League.
"This is a different experience for me and there will be consequences of playing non-league football for the club next season. As for my position, I will have to sit down with the chairman and discuss things."