Valencia was shown a straight red card after crashing through the back of Sebastian Saucedo in the second half of United's 2-1 win in Utah.
But Mourinho refused - leaving the match official with no choice but to send him off.
Saucedo left the ground on crutches and facing a long spell on the sidelines.
Ecuador international Valencia said: "It was my fault. I hope that it doesn't happen in an important competition like the Premier League or the Champions League.
"It was a friendly, but I want to apologise to the fans and my team. I hope it will not happen in the future.
"It was my mistake. The boy was very excited, he wound me up a bit and I hope it doesn't happen in the future."