Stockport had given the south coast strugglers permission to speak to Gannon on Wednesday about the managerial vacancy at the Withdean Stadium following the departure of Nicky Adams by mutual consent.
The caretaker partnership of Dean White and Bob Booker steered Brighton to a 1-0 victory at Millwall on Saturday but there was no repeat at Withdean, where they have now taken only four points out of a possible 24.
Adam Virgo, the match-winner at Millwall, was sent off in the second half, together with Northampton's powerful striker Adebayo Akinfenwa after they wrestled with each other.
It left referee Trevor Kettle little choice other than to show a red card to the pair of them, in Virgo's case his second of the season after receiving his marching orders for two bookable offences at Oldham in December.
Northampton were as desperate for a result as Brighton after falling into the relegation dogfight on the back of four straight defeats.
They took the lead just before the break with a right-foot snapshot on the volley by Ryan Gilligan, the midfielder's third goal of the season.
White and Booker made a double substitution early in the second half, bringing on Craig Davies and French winger Seb Carole.
It paid off immediately, centre-half Tommy Elphick heading the equaliser from Carole's corner.
Davies looped a header against the crossbar from a Jim McNulty cross nine minutes from time.
The Wales international striker then spurned a great chance to snatch victory for Brighton in stoppage time, firing wide when clean through.
The result maintains Northampton's two-point cushion over Brighton in the fight to avoid relegation.