The visitors won 2-1, with Ayoze Perez scoring an injury-time winner. Toni Lato saw red for Mallorca in the second-half.
"It's a big disappointment, after the effort and savouring the point, that goal hurts a lot," said Arrasate.
"We had some good sequences with the ball with ten players. There is little to blame on the team. We did not make the best decisions, neither with the expulsions, nor with the foul that led to the goal, nor with the last defensive action with five defenders.
"In the last play we did lack patience. We managed the rest well. In the first half they were superior because we lost our balance and it was difficult for us. In the second half we were braver in pressing, we got the reward of the goal, and we came close to victory. With 10 men we have to take advantage of the point and think about it."