Portsmouth were reduced to ten men just before the hour mark when David Norris was sent off for a tackle from behind.
Appleton disagreed with Friend's decision, suggesting that the West Ham players were influencing the referee.
"It was not a sending-off, it was harsh. I do not think it was a two-footed challenge and it was not a tackle from behind," said the 36-year-old manager.
"The biggest disappointment was I have never seen a red card pulled out of a pocket so quickly in my life. We were put on the back foot after that. It was not a penalty. It was harsh. I think there was two or three West Ham players refereeing the game. We should have had a handball at the end as well.
"You need the referee to be strong and I do not think he was. I felt some of the West Ham players were having an influence on his decisions."
The win keeps West Ham level on points at the top of the Championship table, while Portsmouth are languishing down in 17th place.