The Reds manager admits a first victory in eight matches has lifted some of the pressure building at Anfield.
Hodgson labelled Sunday's Premier League match at home to Blackburn as a "must-win" game as speculation began to grow that the 63-year-old had two fixtures to save himself from the sack.
Such wild rumours appear wide of the mark and Hodgson refuses to accept his position may be in jeopardy after the £300million takeover by New England Sports Ventures.
"Mass media talk these days says 'lose two games and let's sack the coach and start all over again'," he said after the 2-1 victory over Rovers at Anfield.
"I divorce myself from all of that, it is not something I feel among the players or the staff.
"I'm not certain the people here (NESV) have that type of mindset, they are top sportspeople.
"They took over the Boston Red Sox, who weren't doing very well, and turned them into a champion team."
A number of NESV representatives were in the crowd to see the win, although principal owner John W Henry remained in the United States because of illness.
"There were a lot of people here from the organisation here so I'm pretty sure his (Henry's) phone was buzzing and he'll be pretty happy with the performance," he added.
Sotirios Kyrgiakos and Fernando Torres scored at either end of a five-minute spell just after half-time which saw Jamie Carragher's seventh Premier League own goal briefly even things up.
After their worst start to a season since 1953/54, when they were relegated, a second league victory was very welcome.
But Hodgson admitted the team's lack of confidence as a result of their poor form contributed to a nervy ending having dominated for three-quarters of the game.
He said: "One-goal margins always bring with them an element of relief because even though you know it will be terribly unjust if you don't win the game, football is not known for its justice.
"Things can happen; you can get to the 93rd minute and concede a goal against a team which has not had a shot at your goal - that is a possibility.
"So you are anxious for that final whistle and there was no doubt there was a lot of anxiety in our play in the last 15 to 20 minutes which had nothing to do with what we had done in the previous 70.
"But that was because we were lying in the bottom three at the beginning of the day and we can't get that fact out of our heads.
"We wanted the three points and there wouldn't have been too many of us among the players and staff who would have been disappointed if the referee had blown his whistle when the second goal went in."
Blackburn manager Sam Allardyce felt the absence central defenders Chris Samba (suspended) and Ryan Nelsen (injured), and the loss of defensive midfielder Steven Nzonzi to injury in the first half, cost his side.
"When you come to places like this you want to field your best team - even though Liverpool are not having the best time of it - and I was not able to do that," he said.
"The basis of our success is based on a solid unit defensively but it was far too weak to cope with Liverpool."