Before Carrick's Old Trafford swansong on the final weekend of the league season, United have a Thursday night game at West Ham.
This was perhaps his strongest signal yet.
Mourinho also said there were players in his squad who are not up to United standards, but who he accepted would not be leaving the club.
On the plus side, with one match still to play United have nine more points than they accumulated last season, and second spot is the highest they've finished since winning the title in 2012-13.
"We are the second-best team in the Premier League, a fantastic competition with lots of good teams, with six teams trying to finish first", Mourinho told BBC Sport.
Asked if he needs more quality or a better mindset in his squad, Mourinho replied: "Both".
"He's a top, top player and I think people should show him a bit more love". That is specifically the point of concern for the Portuguese, and he thinks that the team should have played in a similar way when they faced the bottom half clubs. I worked with the players for a couple of years.
"I've got to say I didn't really make much of it, to be honest", he said.
Since the Chilean signed on January 22, Rashford has made United's starting XI for a Premier League fixture on just three occasions - restricting him to only 408 minutes of top-flight action.
United, denied victory by the inspired form of West Ham goalkeeper Adrian, moved four points clear of third-placed Tottenham with one game left.
As a result, Mourinho has axed the pair for the trip to London Stadium to face West Ham United. You buy a central defender you don't like, you buy another one. "In this moment for me, he's staying, yes".
United's record signing has had another inconsistent season and the club's decision makers now want to cut their losses.
"It is not like you always lose against the big teams because you are afraid of them or you always lose against the small teams because you don't respect them".