The Uruguay international scored Liverpool’s second goal, yet clearly handled the ball in the build up, before making it 2-0 to the visitors at Field Mill.
While Mansfield went on to grab a goal back, through Matt Green, it was not enough to save them from being knocked out of the competition, although Radford insists her club deserve a replay.
“It feels like it has been stolen from us. Whether or not it was deliberate, it should be sorted out,” she told reporters.
“It is unfortunate referees and officials can’t pick up these things. We should at least be having a replay.”
Liverpool manager Brendan Rodgers, meanwhile, has defended Suarez, saying the officials saw the incident and decided it was not a deliberate handball.
"It's hit his hand but what do you want him to do in that situation?" he said after the game.
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"I don't think it's even a discussion and I don't think people would ask the question if it was anyone else.
"The ball has popped up, it's hit him and, after that, it is up to the officials what they do. I said to the fourth official straight away: 'Was that handball?' and he said they had seen it but they decided that it was not deliberate.
"It's not his fault. But he has a thick skin and I think people are starting to recognise the ability the boy has. He is a brilliant talent as you have seen him in that little cameo when he has scored one and might have scored a number more.
"He is a wonderful professional and we need to appreciate him while he is here. He loves it. He is a great family man and a great player."