He did accept, however, that any potential bid for a Premier League title was already looking remote.
Having clawed their way back from 2-0 down, the visitors conceded a third time six minutes from the end as Dimitar Berbatov completed his hat-trick.
It inflicted Liverpool's second defeat of the campaign - their first coming at Manchester City a month ago - and Ferguson believes it is a major blow for their season with the club lingering in 16th place in the Premier League.
"[People were saying] it would have been a catastrophe for Liverpool if they had lost, and a catastrophe for us if we had - fortunately we won," Ferguson said.
Hodgson admitted that, with Chelsea stretching their advantage at the top of the table, Liverpool's chances of winning the title were already slim but their aim of finishing in the top four remained alive.
"We have had a remarkably hard start to the season," he said. "Our performance today was clearly a lot better than our last two Barclays Premier League performances (a 1-0 win over West Brom and a goalless draw at Birmingham).
"We were playing against a top team and we can take a lot of credit from the way we went about our business and got ourselves back into the game. To use words like catastrophe is a bit strong unless you are talking about winning the league.
"Of course if Chelsea win today we will be a long way behind them early doors - I suppose you could use the word catastrophe for that, but at this early stage of my time working the club I can't be making those judgments.
"Our aim is to get better, to get to the Champions League, and maybe that is where I have got to have my focus."
United seemed to be cruising after Berbatov struck twice, once with a first-half header and then with a clever overhead kick which went in off the crossbar.
However, Steven Gerrard dragged Liverpool back into the game with a penalty, after Fernando Torres was fouled by Jonny Evans, and a free-kick after the Spain striker was controversially pulled back by John O'Shea, who was only booked.
There was an argument the Republic of Ireland defender should have been sent off for denying Torres a goalscoring opportunity but referee Howard Webb was lenient.
Ferguson accused the Liverpool striker of trying to get his player a red card but Hodgson again refused to bite.
"Definitely Fernando Torres made a meal of it," Ferguson said. There is no doubt he was trying to get the player sent off."
Hodgson saw it differently. "I prefer to talk about the game and talk about issues that interest me," he said. "Sir Alex is entitled to any opinion he wants to have but I'm not going to come here and say I agree or disagree.
"I thought the referee refereed the game very well and I have a very ambivalent attitude to those type of things. I am not a great lover of red cards for petty offences. Alex is a lot closer to it where he sits but my first thought when it happened was 'this is a foul' but I didn't think he should have been sent off.
"My staff around me jumped about saying he should have been sent off but I took a much calmer attitude towards it.
"As it turned out we got the goal anyway and that should have been the goal which got us a good and maybe deserved point, but we defended poorly five or six minutes from the end at a cross which we should have done much better on.
"In my opinion it would be churlish to talk about whether a player should be sent off when really our downfall was due to the fact we should have defended much better for that third goal.
"The first was a wonderful header and the second a bit of genius which is difficult to defend against but the third was far too routine. Having got back to 2-2 we should have kept that."
Ferguson glossed over the defensive frailties his side showed for the third league match running, after conceding late goals in draws at Fulham and Everton, to claim United should have been out of sight before Liverpool launched their comeback.
"From thinking to myself 'it's going to be 10' we ended up at 2-2," he said. "It was a travesty of a scoreline then - but a great result at the end."
Hodgson again disagreed, saying: "I thought United played well but to undermine our performance is a little bit harsh."