The Beckham-backed side suffered their sixth straight defeat as they were handed a 5-0 humbling by New England Revolution on Wednesday night.
It's a result that leaves Miami - who boast big name signings Gonzalo Higuain, Blaise Matuidi, Keiran Gibbs and Ryan Shawcross in their roster - with the worst record of all 27 MLS sides and bottom of the Eastern Conference.
The torrid run of form has piled the pressure on Neville, the former Manchester United Class of 92 defender who was given the job by his old friend, but insisted it had nothing to do with their friendship.
Neville has admitted he knows what the implications will be if his nightmare run at Inter Miami goes on.
But, for now, it is claimed the under-pressure boss still has the backing of Becks who, according to The Sun, is now planning to fly out to Florida.
During their barren run, Inter Miami have scored just one goal and conceded 13.
Neville insists he doesn't need the club's owners, which includes former teammate Beckham, to remind him the results are not good enough.
But he is confident his job is not in danger after just seven months in the role.
"I feel their full support - I always have done," Neville said of Miami's owners.
"They don't need to tell me about their concerns because I have the same concerns.
"I've been in football long enough and I know the consequences - that's no problem to me. We're doing everything in our power, we just need better performances on the field.
"I've got great responsibility and I'm accountable for everything that I do. We're on a run at the moment that puts me under pressure."
Inter Miami boast the likes of Higuain and Matuidi - who share 13 major European league title wins between them - in their ranks but were 4-0 down to Eastern Conference table-toppers New England at half time.
Although his side have been in bad form, Neville claimed the performance took him by surprise and called on the players to give more.
"I wasn't expecting it. The players need to take a long, hard look at themselves, and so do I," he added. "We win and we lose together.
"Ultimately it's my job to make this team better, and in this moment in time they are not. That's on my shoulders.
"When we suffer a disappointment, we need to make sure that we can recover. That's what football's all about - having courage, bravery, not letting your team-mates down on the field.
"We're not doing that and it's something we've not done for the last six games. It's something we have to rectify ASAP.
"Did they have better players than us? On paper, no, but they're a team and that's what we must become. That's all I'm asking for - a team that will fight for each other and look round the dressing room and trust each other.
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"That's what I've asked them to do - look in the mirror and ask, 'what are you doing for the team?' Nothing will deter me from trying to be a success at this football club."
Inter Miami joined America's top flight for the 2020 season, with Neville taking the job ahead of their second campaign after three years in charge of the England Women's team.
He has won just two league games since taking charge and offered his apologies to Inter Miami fans for the performances and results.
"It's the lowest in terms of my feelings after a defeat that I've had since I came to this football club - and we've had some disappointments," Neville said.
"You can lose games in football, but the manner in which we lost tonight was… we've said the word unacceptable in the past - it feels worse than that.
"It's a case of playing for your pride, for the badge, for your supporters - I can only apologise to them for what they saw tonight. It's them that I feel for, more than myself or the players, because they deserve better."