The Spain international was given his marching orders for the first time in a career in which he has played almost 500 games after he picked up two yellow cards within three first-half minutes.
"As you can imagine, it's not easy for me to write these lines," Mata wrote in his blog on the club website.
"The truth is this is a new and strange situation for me, not easy to assimilate, but we learn from everything."
Mata also felt the sending-off was harsh.
"I have the feeling that both decisions were rigorous; that, in many occasions, we see more serious fouls that are not penalised in such a way, but at the same time I could have avoided them and I take responsibility," Mata wrote.
Lifting the Europa League appears to be United's only hope of qualifying for next season's Champions League as defeat at West Brom left them three points behind fourth-placed Manchester City, who have a game in hand.
Louis van Gaal's men travel to Anfield to take on arch-rivals Liverpool in the last 16 of the Europa League on Thursday.