The big talking point of the match came when Juan Mata scored Chelsea's second goal, despite replays showing that the ball did not cross the line.
Redknapp has now added his voice to those calling for the introduction of goal-line technology.
"Atkinson's watched it now and says he feels worse than I do," said Redknapp. "I said, 'I don't think so'. But he says he feels bad.
"He knows he's made a mistake and he says he'll have a bad week as well. He's just made an honest mistake. He's not done it on purpose. There's nothing we can do about it now.
"Goal-line technology has to come into the game. You can't keep having situations like that. You can't carry on like this, with important decisions not being correct."
Chelsea will now face Liverpool in the FA Cup final.