"I always knew it would be a difficult job, and it's not an auspicious start but that's how it goes in football. I am disappointed, I was a bit deceived as I thought we would do better," he said.
Following Sunday's 3-2 Premier League loss to Manchester United, Hodgson made several changes to the side, but he said the players selected should have been good enough to beat the lowest-ranked team left in the competition.
"These are players brought to the club, some of them very expensive with big reputations - maybe I don't know them well enough yet, certainly they haven't done themselves too many favours in my eyes," he said.
"When you've got a squad with players who have come here for big money, this was a chance for them to show they're great players - unfortunately, and full credit to Northampton, we weren't good enough to beat them."
Hodgson said it was only in the last 15 minutes of extra time, when they were trailing 2-1, that the team showed any fighting spirit.
"When it goes to penalties and you are at home and in front of the Kop your hope is that at least the players will have the composure and confidence to win the penalty shoot-out, but we didn't," he said.
"All I can do is congratulate Northampton and apologise to everyone; the fans came expecting to see us win and I expected us to win but it wasn't to be.
"These players have to accept responsibility. I accept responsibility for changing a lot of players in the team, I did it because I honestly thought the players I put on the field were good enough to win the game and they weren't.
"The obvious conclusion to that was I shouldn't have changed that many players but we should have been strong enough to get a result.
"We must all take our responsibility. I am just bitterly disappointed that the team I had so much faith in did not repay that faith this evening with the exception of one or two performances."
Few would have predicted the events that followed after Milan Jovanovic slotted in to hand Liverpool the lead inside 10 minutes.
But goals by Billy McKay and Michael Jacobs looked to be sending Northampton into the fourth round before David Ngog's equaliser close to the end of extra time set up the spot-kick drama.
Up stepped Abdul Osman to slot home the crucial kick from 12 yards to secure a magnificent victory for the team sitting in 17th spot in League Two.
Cobblers chairman David Cardozo hailed the win at Anfield as the greatest in the club's history.
"I thought we were the better side for long periods, the fans were amazing and did us proud and hopefully we did them proud too," he told BBC Radio 5 live.
"I think this has got to be the greatest night in our history."
Cardozo added: "I'm in the car park at Anfield, drenched in rain, preparing to drive back home and I'll have a good dance in the car."
Cobblers manager Ian Sampson was equally delighted after steering his side to victory.
"What a fantastic night," he said. "They should be so proud of their performance. The spirit they showed was tremendous.
"I was disappointed it went to penalties because I felt we deserved to win in normal time but the players who stepped up deserve tremendous credit and they showed real character to take a penalty in front of The Kop.
"Northampton have never won here before, and it might never happen again, so this is a night to savour and enjoy every last minute of."
Sampson added: "The difference between a club like Liverpool and Northampton is vast but there have been cup upsets in the past and I'm just absolutely thrilled for everyone that we managed to pull it off.
"We tried to pass the ball and I think we dominated the game for long periods. It doesn't get any better than this and for me this is right up there with the games at Wembley.
"The lads are absolutely buzzing and they've told me that they want Manchester United at Old Trafford in the next round."
Sunderland are next up for Liverpool in the league on Saturday, and Jovanovic told BBC Radio Merseyside: "For us now every game is really important because five points from five games is not enough.
"I hope now we're though this difficult period and in the next three or four games we can collect maximum points."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.