Jordan Ponticelli scored a late equaliser for the 10-man Red Dragons but it was not enough.
Jordan Ponticelli gave the Red Dragons hope late on, but they slipped out of the top seven on the final day.
Shaun Pearson headed over Dagenham goalkeeper Elliot Justham’s crossbar, while Will Wright missed the target twice for the hosts.
Dagenham almost scored just before half-time, but Paul McCallum’s header from Angelo Balanta’s cross was cleared off the line.
McCallum found the net six minutes after the interval, tapping in Balanta’s ball across the box for his 10th goal in as many games, before Wrexham were reduced to 10 men shortly after when Paul Rutherford was sent off for a poor challenge on Matt Robinson.
Wrexham set up a dramatic finish when Ponticelli netted from close range, but it was not enough as they missed out on the top seven by one point.