Mourinho criticised Smalling for not putting his body on the line through an injury while other players were doing so.
However, the England international explains that Mourinho's comments were born out of frustration with the injury crisis at the club.
When asked if Mourinho apologised, Smalling said: "No. It comes back to the manager's frustrations, as well as ours.
"When I'm sitting down with the manager and the medical staff we set out a timeline and then we try to shave it and push and push. That's what we are always doing because the longer it takes to recover from an injury the fewer games you play.
"The manager has shown his frustration but we are just as frustrated. They are always trying to push us as quick as we can."