Carrick played 90 minutes for United at Fulham on Saturday but will not join up with Roy Hodgson's side due to a hip injury, while Defoe was forced off in Spurs' win over West Brom with an ankle problem.
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“He is definitely out of the England squad and our Newcastle game for sure,” Villas-Boas said to Sky Sports.
“We just have to scan it, but at the moment it doesn’t look too good. Normally it is the ligament on his ankle and this should keep him out for around three weeks.”
England Under-21 manager Stuart Pearce has also been hit by a raft of withdrawals ahead of his team's clash with Sweden.
Manchester United defender Phil Jones, Liverpool starlet Raheem Sterling, Southampton's Nathaniel Clyne and Norwich centre-back Ryan Bennett have all dropped out ahead of the game at the Bescot Stadium.
A Football Association statement confirmed that no replacements have been drafted into either squad.