Suarez scored what turned out to be the decisive goal in a 2-1 victory for the Premier League side when he handled the ball before shooting in from close range.
Liverpool manager Brendan Rodgers insisted after the final whistle that the handball was not deliberate, but Radford thinks the Uruguayan cheated and should feel ashamed.
"When you get a professional player like Suarez and when they celebrate after a deliberate foul, then of course it hurts," said Radford.
"Obviously he was (gloating). It was like, 'Hang on, I can get away with this'. If one of my players had done that, I'd be embarrassed.
"I was looking for a fair and true competition. That was one incident in the game that made me feel like it was such a killer.
"They've denied us a replay but it doesn't matter. I'm big enough and daft enough to stand up for the club and take us forward.
"But it's hurtful for the league we are in. I'd have been embarrassed and the man should be embarrassed.
"To do it deliberately and then celebrate is the hardest thing. To cheat, OK, but to cheat and then celebrate cheating... that is the worst thing you can do.
"Cheats will never prosper. The Liverpool directors felt embarrassed."
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