Carrick impressed after taking over as interim boss following Ruben Amorim's acrimonious exit in January, leading United to Champions League qualification.

He was rewarded with a two-year permanent deal, but results have nose-dived in this campaign.

The Red Devils are in the Premier League relegation zone after winning just one of their 10 league matches so far.

The Old Trafford club named former Tottenham, Chelsea and Paris Saint-Germain boss Pochettino, currently USA head coach, as their new manager on Friday.

Despite the downturn this season, Carrick remained popular with supporters in part for his role as a player in multiple triumphs under Alex Ferguson, who retired in 2013.

The 45-year-old said his affection remained rock-solid.

"I want nothing but success for Manchester United. This club has been such a big part of my life and that will never change," Carrick wrote in an Instagram post.

"I'll always be proud to have played my part and I'll always want the very best for it.

"I'll be right there with you from now on, watching from the sidelines, cheering the lads on."

The former England midfielder paid tribute to the fans, his coaching staff and United's players.

"I've had the immense privilege of leading Manchester United, the football club that I love," he wrote.

"There are very few who get to live that and feel it, and for that I'm incredibly grateful. With that comes huge responsibility, and to be at Manchester United, you need to understand exactly what that means.

"It's different to anywhere else. Ultimately, you need to push to be the best, but there is a culture, there are values and there are behaviours that you have to live by and respect, which have been built over a long period of time.

"It's a football club that is unique, with substance and history that cannot be ignored. This is what inspired me every single day."

Carrick described United's fans as a "special, rare breed".

"We've had some great times this year and moments we'll all remember," he said. "The best thing about being in my position was seeing so many of you lose yourselves in the emotion of those moments, leaving the stadium desperate to come back again next time.

"I just wanted to give you something back. That love never dies."