Hodgson sorry after shock defeat
The npower League Two side, the lowest-placed club in the competition, recovered from Milan Jovanovic's ninth-minute goal to lead 2-1 with goals from Billy McKay and Michael Jacobs with just four minutes of extra-time remaining.
David Ngog nicked a headed equaliser but the Cobblers prevailed in a penalty shoot-out.
With a Barclays Premier League title bid unlikely again this season, the Carling Cup was seen as a trophy the Reds should be looking at winning.
Combined with their poor start to the league campaign, sitting in 16th place after just five points from as many games, Hodgson admitted: "We wanted to do well in the Carling Cup and we haven't done.
"We were given a kind draw against a team three leagues below us, were expected to win and when you don't you can expect to be criticised from the top downwards.
"It is a major setback for the club. The Carling Cup is a competition we are capable of doing well in and we were playing lower-league opponents.
"Whatever happens, if it doesn't result in a victory it is a very negative thing and a setback for the club, one of many we are facing at the moment."
The 62-year-old, who made several changes from the side that lost to Manchester United at the weekend, added: "All I can do is congratulate Northampton and apologise to everyone."