The Three Lions have gone through nine managers, including three caretakers, in the 26 years Sir Alex spent at Old Trafford, reaching just one semi-final during that time.
And Carrick believes a similar approach from the national team would only help their fortunes, saying it "breeds comfort".
"I think stability helps at any level of football, whether it is club or international" the 31-year-old told reporters. "Take David Moyes at Everton, look at what he has achieved being there for a long time.
"It breeds a comfort and everyone knows where they stand, you can get a bit of continuity."
After celebrating at fifth Premier League winners' medal last season with the Red Devils, Carrick insists the players are already looking forward to defend their crown next term under new boss Moyes.
"What's done is done now," added the former Tottenham and West Ham midfielder. "We've moved on from that already, looking towards these games and next season, you can't look back for too long.
"You can enjoy it, we've enjoyed it, we've celebrated, but we've celebrated enough now and it's time to move on."