The Florida-based side had opened the new campaign with two victories, over Montreal Impact and Philadelphia Union.
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Now, though, a woeful run of results has hit the club, formed in 2018, culminating in a 1-0 defeat to Houston Dynamo.
Inter Miami had 20 shots to Houston's 11 but still found themselves on the losing side due to a Daniel Steres goal 18 minutes from time.
With losses piling up, so is the pressure, despite Neville's ex-Manchester United teammate, Beckham, running the club.
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But the ex-Lionesses manager insists the results are a true reflection of performances and backs his side to come good.
He said, via The Athletic: "You're right. We need to start winning. We can't hide behind the fact that a six-game loss is good enough. It's nowhere near good enough for what we want for this football club.
"I take full responsibility for that and the consequences that come my way. But I believe 100 per cent that we can start winning, we can start getting wins on the table, we can start climbing the table.
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"I've got belief in the players we've got. I see it. I see it every day in training, I saw it tonight more than ever.
"If you look at the games, we didn't deserve to lose in Cincinnati, we didn't deserve to lose in New York City, we didn't deserve to lose tonight, we deserved to win the game tonight. So we've got to keep believing in what we're doing.
"In terms of the support, I've always had support from this [front office]. I've been in football long enough to realise that, with this title, along comes pressure and expectations and demands. And I'm big enough to take that and handle that."