A goal from Handling had cancelled out Lewis Macleod's opener at Ibrox and led to a period of dominance for Hibs before the referee, John Beaton, ruled that a challenge on David Templeton by the visiting forward in the 79th minute was worthy of a red card.
"The sending-off changed the game," said Stubbs. "We were in the ascendancy at the time and I felt we were going to go on and win the game. I thought it was harsh. More often than not, I think a yellow would be sufficient, but the referee sees it differently."
Stubbs refused to go into further detail on Beaton's decision, making a somewhat cryptic comment to the time he spent as a central defender at Celtic.
"I am not going to get into that one," he said. "I had five years of it."
Ally McCoist, the Rangers manager, showed little sympathy for Handling. "It was a poor tackle," said McCoist. "Whether a sending-off or not, the referee was nearer than us."
Farid El Alagui missed two excellent chances for Hibs at 1-1, but believes the Edinburgh side proved a point.
"Before the red card, we played better than them," he said. "If you come here with nothing to fear and try to play football, I think they cannot handle it."