The Penwortham-based official sent-off Exeter defender Dean Moxey for a reckless lunge on Kevin Watson in the 59th minute.
It was 2-0 at the time of the red card and Northampton went on to complete a comfortable victory - inflcting a third play-off final defeat on Exeter in four years.
Northampton had finished seventh in League Two - unweighted points per game used after the season was curtailed - seven points behind fifth-placed Exeter.
They had lost the first-leg of the semi-finals 2-0 to Cheltenham but roared back to win the away leg 3-0.
Last night's red card was the 10th shown by Mr Salisbury in his 29 games this season.
He had no choice but to dismiss Moxey, the defender's challenge two-footed and late.
The fourth official at Wembley was Leigh Doughty from Freckleton, with Blackpool's Natalie Aspinall the reserve assistant referee.