Two goals from Benjani Mwaruwari, who had not started since November 6 and scored once in 12 previous appearances, and Martin Olsson condemned the Reds to a ninth Barclays Premier League defeat of the season despite an 80th-minute consolation from Steven Gerrard, who missed a late penalty.
The result seems likely to hasten the end of his six-month reign at Anfield, with owners New England Sports Ventures having already begun their search for a replacement.
Hodgson answered just three questions in his post-match press conference, which uncharacteristically for him lasted just over two minutes, and as soon as the subject of his position was broached proceedings were brought to an abrupt halt.
"I am not prepared to talk about that because obviously I am depressed enough with the performance and the result," said the 63-year-old.
"I have no comments to make and I have no intention to answer any questions on the subject."
Asked about his feelings after the defeat Hodgson said: "Dejection, bitter disappointment, frustration.
"I am very disappointed for the fans who gave us good support and saw the team concede the goals we did.
"I thought in the second half we did well to retrieve a seemingly hopeless situation and get back on track and had Steven's penalty gone in who knows, we may have made the last five minutes more exciting.
"Unfortunately when you are Liverpool and you lose away to Blackburn there is nothing that can be said which will put a positive slant or make the situation look any brighter.
"As far as I am concerned it is a really bad day and there is not much more I can say other than, to the fans, that anything they are feeling tonight I can assure them the feeling is equally as bad and equally as depressed in the dressing room.
"Tonight was a performance anything other than the performance we wanted to give."
Rovers boss Steve Kean, who marked his first home victory since taking over from the sacked Sam Allardyce last month in some style, felt he could not really offer Hodgson any sympathy.
"Roy is a great coach and manager but we can only look after what we can do, which is winning games to try to move us up the league," he said.
Kean, who was missing eight first-team members, paid tribute to the players he had available.
"I thought we were tremendous tonight," he added.
"We let them back into the game and it was a bit nervy when we gave them the penalty but overall, on the balance of play, we were worthy of the three points.
"It was all about the togetherness; there is a tight group and we were down to the bare bones and that is how you show team spirit.
"I don't think it is anything about me tonight it is about the team and showing what we are as a club and I am really proud of the lads."