Schweinsteiger and Schneiderlin joined Man United earlier this month, costing around £15m and £24m respectively.
The new signings mean that Carrick may not be an automatic pick for Louis van Gaal in the upcoming campaign.
However, the English midfielder has insisted that he is delighted with the added quality in the middle of the park.
“You want the best players here, and it’s good for the squad, for the team,” Carrick said.
“Morgan is a good player. He has done terrific. It’s another step for him in his career and there’s no better place to be.”
“We all know what Basti brings. He is a terrific player and he’ll have a big influence on us going forward.”
Carrick proved to be an indispensable asset last season. His unflappable composure in the holding midfield role gave van Gaal’s side license to dominate big games. If anything, the Dutchman was over-reliant on the midfielder; when Carrick suffered an injury against Manchester City, United’s form faltered as they only managed one win from their last six games.
The England international is becoming increasingly injury prone, leaving United’s midfield somewhat destitute. As Carrick celebrated his 34th birthday on Tuesday, United fans will know that the midfielder won’t be around for much longer, and certainly won’t be able to play every game next season. Schweinsteiger and Schneiderlin, two tough, reliable battlers in midfield, were introduced to combat this issue.
Carrick, when he does play, will help Schweinsteiger and Schneiderlin by allowing them more time on the ball, providing a solid backbone for the two to thrive upon.