The Ghanaian star, asked to play at right-back due to Chelsea's injury crisis, found himself booked after just 12 minutes for a foul on Alvaro Arbeloa.
But in a match that produced nine yellow cards from under-fire Hampshire official Rob Styles, Essien thought he had received a second yellow card from the referee in a fractious second period.
In fact, although TV replays showed Styles waving a yellow card over Essien's head it turned out that it was John Terry who was being cautioned for dissent.
Mourinho said: "Michael was honestly very frightened, he thought he had been booked again.
"The referee then explained that he had only booked one player, John Terry, but Essien stood there for a long time and he said afterwards that he believed he had been cautioned again."
That incident summed up Styles' afternoon, in which he came under fire from both sets of players and was accused by Liverpool skipper Steven Gerrard of "cracking" under pressure when he awarded a penalty for a supposed foul by Steve Finnan on Florent Malouda.
Liverpool were ahead through a first-half strike from Fernando Torres, but Gerrard believes Styles blundered with the penalty equaliser, netted by Frank Lampard.
Gerrard said: "I don't want to say too much because I will get into trouble, but the referee didn't play well.
"Whether it was because the Chelsea players were talking I don't know, but in the end he's cracked and made a bad decision. It wasn't a penalty and I hope he comes out and says sorry now.
"We have to apologise as players if we make mistakes so I hope he does the same."
He added: "There were so many positives from that performance, though, and I really think it shows we can challenge this season.
"The goal was excellent. I managed to slide the ball into Fernando's path and he showed great quality to finish it off. More of the same please, Fernando!"
Gerrard also revealed he will have an x-ray on Monday on his fractured toe to determine if he can play any part in England's midweek friendly with Germany on Wednesday.