Scunthorpe looked set for victory when centre-back Niall Canavan added the finishing touch to an inswinging corner from Andy Dawson to open the scoring after 52 minutes.
Six minutes later the visitors were reduced to 10 men when skipper Ricky Ravenhill was sent off for a second bookable offence.
But Northampton came fighting back with a 66th minute equaliser when centre back Zander Diamond headed home a free-kick from Darren Carter.
"At the moment it is difficult to feel too positive about equalling that club record," admitted Wilcox, whose team have not been beaten since he took charge at the end of November.
"When I have time to reflect on it properly I will see it as an outstanding achievement by a group of players who are so committed to the cause.
"But at the moment this is the most disappointed I have felt since I took over as manager here. And the players are disappointed too.
"Our first half performance was not good enough.
"I thought our play was laboured and we did not pass the ball quickly enough.
"I wanted us to be more offensive on the ball, get the ball wide and create more pressure.
"We did that much better in the second half and got ourselves into the lead.
"But we talk about managing periods of the game and it was the next period we did not handle very well after they had a man sent off.
"Credit to Northampton, they made life difficult for us when they were down to 10 men but the only way I could see them scoring was from a set-piece.
"And that's exactly what happened when we got sloppy from a free-kick."
Scunthorpe will now try to set a new club record of 20 games unbeaten when they are at home to Southend on Tuesday night.
"I won't be asking for a response from my players after this result because the response they have given me since I first took charge at this club has been magnificent," said Wilcox.
"But I will certainly be looking for a better first half performance from them."
Northampton boss Chris Wilder was delighted to go away with a point as his side continued their revival with just one defeat now in their last six games.
"My team gave me everything," he declared, "especially when we were down to 10 men.
"Losing Ricky was a blow to us but we dug in and whether we deserved a point or not, we got it.
"It's important for us to try and keep our run going and keep the level of confidence high.
"Coming here to Scunthorpe we would certainly have settled for a point before the start.
"We knew it would be difficult because Russ Wilcox has done a magnificent job to take them 19 games unbeaten.
"In the first half I thought we were well in the game.
"I expected a response from Scunthorpe in the second half and they gave one.
"They put us under pressure but I did think our goalkeeper was impeded when they got their goal from a corner.
"I was delighted with our equaliser from Zander Diamond and we then hung on for a draw.
"When we got another free-kick in injury time I was trying to urge Zander forward again, but I cannot blame the players for wanting to settle for the draw."