United will host Aston Villa at Old Trafford on Sunday as they seek to push away from the relegation zone after a horrid start to their campaign.
Seven games without a win in the Premier League and having just one Premier League win to their name this season, United are desperate for three points as they fight away from home.
Speaking to NBC Sport, Neville warned Carrick, who is under a huge amount of pressure, to focus on the core of his team rather than experimenting with youngsters against Villa.
"I wouldn’t say it’s time to play kids, it’s a time for experience. I think it’s something you do when you have talented kids for a start but when you’re absolutely desperate. This is a time for him to put his best team out on the pitch and they’ve got to go and deliver.
"Sitting in the bottom three it’s incredible to see that, it’s sobering. What that night was on Wednesday was emotion. Manchester United got that goal and in European nights you’ve seen that before where the emotion carries you through wave after wave of attacks. The atmosphere is electric but that isn’t going to get you through all the difficult moments.
"You need performance, you need patterns, you need methodology as a player you need something to consistent and a default style of play. Manchester United have been really, really poor this season. If they go into the international break in the relegation zone it would be a desperate, desperate situation."
The Red Devils' nine-game winless run was ended by beating Roma 3-2 in the Champions League and Carrick will hope his side can carry that momentum to Villa Park.
United have won 42 and have lost just six of their meetings with Villa in what should be an intense test.