The Swede left his job after guiding England to the quarter-finals, just as he had done in the previous World Cup and Euro 2004.
For most pundits, the record leaves Eriksson open to criticism, especially over his tactics in crucial games.
"Sven can be very satisfied with what he did for England," said Carrick.
"Reaching three quarter-finals is not an easy thing to do, history proves that.
"You can't please some people until you win something. But England have only ever won one trophy, so by no means should people just expect us to win things pretty easily.
"Sven has been successful everywhere he has been, and I include England in that."
Despite a clear affection for Eriksson as an individual, there will be no love lost at Eastlands on Sunday as Carrick and his United team-mates look to record their first win of the season at the expense of the Swede's new charges.
"We want the points," he said.
"We want to get back to winning ways and put a run together. We want to be sitting on top of the table not where we are at the moment."