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Cunha also mentioned the "noise" around United when he spoke to BBC Match of the Day.
Neville is a significant part of that noise, either directly or through his growing media empire.
Carrick has previously said he can shut it out.
It cannot be quite so easy though when United fans - who usually back their team through disappointment - followed up chants on Wednesday in disgust at the Brighton debacle by here booing Carrick's decision to take off popular England midfielder Kobbie Mainoo 11 minutes from time.
"There's always going to be certain reactions when you're making changes," said Carrick. "I've spoken to Kobbie after the game and he's absolutely fine.
"I understand at times when we are chasing the game, everyone's a little bit emotional. The supporters are, as well they should be, desperate for us to do the right thing.
"But I don't take any negatives or offence to it. I think we've just got to try and keep doing the right things to get back into the game.
"The supporters were unbelievable today, I have to say, all the way through, and stuck with the boys and supported them. At least we've given them something small at the end to take from it, and I'm sure there's more to come."
And that is the key point.
A draw at Fulham is "something small" considering the home side started the game at the foot of the Premier League - and have now swapped places with Tottenham.
Five points from five games leaves United 12th, an incredible 10 points behind pacesetters Manchester City already.
Their £70m summer signing Carlos Baleba is still to make his debut, and long-term injury victim Matthijs de Ligt was not involved at all, even though both were part of the squad that travelled south on Saturday.
Striker Benjamin Sesko also missed the game after suffering a recurrence of the shin problem against Brighton that he was troubled by for an extended period last season before submitting to a recovery programme that ruled him out for more than three months.
Carrick says "at this point" the extent of the damage is unknown.
This would all be pretty underwhelming were it not for the ticketing issues instigated by the club's touting crackdown that has annoyed so many in the fanbase.
On Wednesday, United will release their full-year financial results to 30 June, around which the full extent of their current debt will be revealed.
Then there is the general debate about the wisdom of new stadium, which is set to cost in excess of £2bn, with planning permission potentially submitted with the main Old Trafford masterplan, which is earmarked for late 2027 or early 2028.
Little wonder, after leading United back to the Champions League so unexpectedly last season, Carrick is presiding over a club whose supporters feel deflated, even if he does not recognise that.
"It's still a big season ahead," he said. "It's a long season and you're going to have spells through a season. That's part of the journey.
"It's not a sprint, it's a long effort.
"I'm not playing it down, you know. We wanted more points, so I'm not saying everything's great. I understand the frustration. We wanted to be better and we wanted to do other things.
"But deflation is certainly not what we have within the club and within the group. The players didn't have that on the pitch today and that's what will carry us through the season without a doubt."
