Alfreton Town's season in the North division was axed after clubs voted 24-19 in favour of null and voiding the campaign.
"I'm a football guy and I would prefer that we were all playing football," Mr Ives told thge BBC this week.
"But I think it's fair to say that in order to do that, teams need somebody to play.
"What was perfectly clear is that teams were struggling due to the financial situation they were in.
"Some were able to fulfil their fixtures and some weren't so something had to be done."
Clubs in the North and South voted to null and void after £10m of National Lottery funding - in place to compensate lost match day revenue from no fans being allowed to attend - ended in December.
Clubs were offered loans to continue but many did not want to take on debt.
The Department for Digital, Media, Culture and Sport claim the grants would only last three months (October to December) but the National League and clubs felt they were led to believe support would be in place until the return of fans.
"The league, together with the Football Association, were under the impression that continual support would happen and they went into it with all good faith, as did the clubs," added Mr Ives, who moved to the National League from his previous job at the FA after former CEO Michael Tattersall stepped down in early December.
"The clubs themselves ended the season and I really feel for the clubs."But I also feel for the league board. We entered into a situation, I've looked in the records, with the best of faith."
Alfreton were not among the 18 clubs in the North and South who are calling for an alternative league to be created for teams that wished to continue.
Mr Ives said: "I think it's in the best interest of the league that we should listen to all the clubs, either side of the fence.
"A very well-crafted letter was put to the league on what might possibly happen. Do I believe we should consider that? Yes, I do."