United produced their most convincing display of the season as they overpowered Hull 3-0 in a one-sided contest on Saturday in which Van Persie responded to his critics with a fine goal.
Van Persie's form has been indifferent this season and he came in for heavy scrutiny after an ineffectual display - in which he touched the ball just 13 times - in United's unconvincing win at Arsenal on November 22.
But a week made a big difference and he repaid the faith of manager Louis van Gaal with a much-improved performance as Hull were swept aside
The 31-year-old threatened on a number of occasions and teed up a goal for Wayne Rooney before capping victory with a powerful left-foot strike.
He left the field to a good ovation as he was replaced by fit-again Radamel Falcao - whose availability might have threatened Van Persie's place - for the final 20 minutes.
Carrick said: "We all get criticised at certain times and it's something you have to deal with
The best way to answer it is the way he did it against Hull.
"Robin scored a great goal and hopefully that will be the start of a good run over the weeks to come.
"When you have got him scoring, Wayne scoring and Falcao coming off the bench and nearly scoring, we'll be a threat to anyone
You want those boys when they're flying and it's scary to play against.
"What Robin and Wayne did against Hull, we've seen that happen so often in the past and hopefully we'll see that in the coming weeks again
It gives the whole team huge confidence and belief that, even if we're not playing great, we're always in the game."
The victory over Hull also changed the perception of the United side as they adjust to life under new manager Van Gaal.
It was their third win in succession - the first time this season they have achieved that feat - and came in such a convincing manner that confidence could only be lifted.
As United toiled last season it was said their reputation was no longer intimidating opponents, but Carrick is hopeful the current team can restore the lost aura.
The 33-year-old said: "I think everyone in the stadium felt it was a good performance and that's the sort of standard we want to be at - dominating teams and winning.
"We've done it in the past but the past is the past
We need to do it again and hopefully as time goes on we can carry on like this and that fear factor will creep back."
United will soon get the chance to put that to the test as they host Stoke on Tuesday night.
Carrick said: "Arsenal was a huge result for us, but the performance wasn't great
We got the performance for long periods against Hull, winning comfortably in the end, so we will look to keep that going against Stoke.
"But we can't look too far ahead
We've never done that
We've never said, 'Right, we need to go on a 10 or 15-game run'
It's bit by bit."
Van Gaal's bid to lift the club after last season's relatively dismal return has been hampered by a lengthy injury list.
Record signing Angel Di Maria became the latest addition to it when he pulled up with a hamstring problem on Saturday.
But after spending £150million on summer signings, United do have strength in depth.
Carrick said: "We believe we can have a really good season but it's been a strange start in many ways.
"Hopefully we can get the injured lads back fit
We had a couple of lads struggling on Saturday but when you can bring the likes of Falcao and Ander Herrera on it does give you confidence.
"That's the beauty of having this strength
You have players to choose from, despite the injuries."
Carrick himself only returned to action a month ago after suffering an ankle injury in the summer.
He said: "That was only my third start in seven months but I felt fine
It's just a case of getting back into the swing of things and finding your rhythm really
Hopefully the more games I have the better I'll get."
Source : PA
Source: PA