Spurs were looking to pay the fee in two instalments rather than the full price up front. This angered the Toffees boss, who has now branded it "insulting".
Moyes told reporters: "We have had an offer from Tottenham of £250,000 which we received on Saturday afternoon. Then it was upped to £500,000 on Monday morning.
"I think that is insulting. It was £250,000 on Saturday afternoon when I was leaving the ground and they upped it to £500,000 on Monday morning. That was £250,000 now and £250,000 paid in a year's time.
"I think it is as surprising an offer as I have known in my career. I spoke to Harry on Saturday afternoon. He made the bid. We had a bit of banter about horses and things. There has been a lot of people saying things, but Saturday at 4pm was the first time we had an offer."
Redknapp was keen to add the services of the 34-year-old to his team as he looks to push on in the league and progress as far as they can in the Champions League.
Moyes was already annoyed with Spurs for making their interest in Neville known after Everton chairman Bill Kenwright told his counterpart Daniel Levy that a bid would not be welcomed.
Moyes added: “I think an offer like that for Everton's captain is a disrespectful offer to the club and I think it is a disrespectful offer for a player of Phil's qualities. I could understand it if he had six months to go on his contract, but he has 18 months to go and he has played more or less every game for Everton this season."
Spurs only made one major signing in January, which was Neville’s former team-mate Steven Pienaar. They have also tried to bring in the likes of Sergio Aguero and Fernando Llorente, but had £38 million and £25m bids rejected respectively.