Frank Lampard's late penalty cancelled out Evgeni Konoplyanka's opener, but right-back Johnson came away from the game unhappy with referee Cuneyt Cakir.
Johnson's booking means that he will miss England's clash with San Marino next month, as will captain Steven Gerrard after he was sent off late on.
"Some of the decisions were crazy," said Johnson.
"I clearly played the ball when I got booked – it wasn't even in doubt. It was the same with Steven's one but he gets sent off. There was a lot of frustration with the officials.
"If you deserve a booking then you take in on the chin but when it's a silly decision like that you get frustrated. Both Steven and I will miss the next game now but we just have to get on with it."
The Three Lions play San Marino on October 12.