Ex-captain Michael Vaughan strongly criticised the team after they were bowled out for 167 in the first innings of the first Test in Dunedin and allowed New Zealand to establish a 254-run lead. Vaughan claimed England's mindset had been one of over-confidence and that they were not "prepared to do the hard yards".
After that, England battled back to save the match with hundreds from Alastair Cook and Nick Compton and half-centuries from Steven Finn and Jonathan Trott. Moores told BBC Radio Five Live's Sportsweek programme: "The disrespect, I don't really agree with that."
He added: "I can see where Michael is coming from, that you go in thinking you are going to win. But it is a sub-conscious thing rather than a conscious thing, because they are all saying the right stuff.
"I think they would have physically trained the same. What they wouldn't have done is been as mentally switched on for a really tough contest. Then you get your fingers burned.
"Then they have kicked back and shown what a good team they are, in many ways, with Compton and Cook up front and people like Finn chipping in with the bat."
England will now hope to make a stronger start in the second Test in Wellington, which begins next Thursday.
Moores said: "They'll be happy to start with a draw because they are still very much in the series and I think they will back themselves, now they have played a game, to win at least one of the next two Tests.
"I think they will be quite happy with that."