Roy Hodgson labelled Liverpool's merited 2-0 defeat in front of their new owners in the 214th Merseyside derby as the best performance of his brief and increasingly tortured reign as manager yesterday – despite a loss that leaves them mired in the relegation zone.

On a day when Liverpool should have been celebrating a new dawn, the scale of the Anfield rebuilding task was laid bare by John W Henry, who hit back at Tom Hicks's allegation of being the victim of "an epic swindle" by claiming £300m was not cheap for a club in need of a major overhaul.

Liverpool were again woeful as an injury-plagued Everton side secured their first derby win in four years through goals from Tim Cahill and Mikel Arteta. The result left the Anfield club level on points with the bottom side West Ham United and their manager cutting an angry, frustrated figure afterwards. He has statistically the worst record of any Liverpool manager after eight league games since George Patterson in 1928.

Hodgson said: "We suffered at the hands of an early onslaught which you invariably do at Goodison but towards the end of the first half we started to even things out. From what I saw I thought we dominated the second half totally. I thought the shape of the team was good today, the quality of our passing and movement was good.

"We didn't score goals and Everton did but I refuse to accept that we were in any way outplayed or any way inferior. I watched the performance and the second half was as good as I saw a Liverpool team play under my management that is for sure."

Liverpool's performance did not bring the catharsis expected following the takeover by New England Sports Ventures on Friday. Itsprincipal investor, Henry, and other associates were present at Goodison Park and, speaking before the sorry display, had admitted that Liverpool are in need of major rebuilding on and off the pitch.

Henry, who along with Tom Werner met the Liverpool squad on Saturday morning and will hold talks with supporters' groups today, said his first impression of the club was: "How much work this is going to be. How steep the learning curve is going to be." He added: "This is not going to be easy. If I could leave just one message it is that we realise the challenge that lies ahead if we are going to go toe to toe with three other big clubs. You look at match day revenues, revenues in general, these guys [at Liverpool] have done a tremendous job of increasing revenues, but you look at the network that [Arsène] Wenger has. I have spent the last two months doing due diligence. We have got our work cut out."

Hicks, NESV's predecessor as Liverpool owner, had argued that the £300m deal between the Liverpool chairman, Martin Broughton, the Royal Bank of Scotland and the owners of the Boston Red Sox had been "an epic swindle". But Henry retorted: "As you do due diligence, if you are really diligent you are trying to find everything that's wrong. There were big financial issues but in the end we made a decision we really wanted to compete at this level. I know some people are saying this was a cheap price. There is no way we look at this as a cheap price for this club."

Victory lifted Everton to 11th in the Premier League table and Moyes admitted that his side's superiority was a reminder to Liverpool that money is no guarantee of success. The Everton manager said: "Seamus Coleman created the first goal. He cost us £60,000 from Sligo Rovers. It isn't all about money and if you wanted football to be all about money I don't think you would enjoy it.

"Am I jealous? Yes, because I want my team to be at the top but I wouldn't swap my chairman [Bill Kenwright] for anyone from America, Saudi Arabia or wherever. He is a supporter and he has backed me and stability is very important at any club."

Moyes admitted: "we conceded possession to Liverpool after the second goal but I was happy to do so because, like us, they have not been scoring freely. We have played better in all of our games this season with the exception of the Newcastle defeat."

Hodgson, however, denied that his Liverpool players looked under pressure, with the exception of Fernando Torres – "He is going through a bad time but we get out of it by keep working" – and insisted: "This is not a crisis."

He added: "The dream was we would come here on the back of new owners and win the game but there is no point in attempting to analyse dreams. This would have been the ideal opportunity to turn things around on the back of the positive entry of the new owners and to get a result here would have been Utopia."