Cox, though, was left "gutted" for the club and his players at the 59th-minute handball from Suarez that clinched Liverpool's place in the fourth round of the FA Cup at the expense of the non-league Stags.
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Debutant Daniel Sturridge, a £12million buy from Chelsea in the past few days, set the Reds on their way to the 2-1 win with a fine eighth-minute opener.
As Liverpool boss Brendan Rodgers pointed out post-match, his side should have been "out of sight" before Suarez's introduction as a replacement for Sturridge four minutes prior to his decisive second goal.
Matt Green gave the Blue Square Bet Premier side hope 11 minutes from time but it was not to be, leaving Liverpool to go on to another tricky tie in the last 32 at npower League One Oldham.
It was Suarez, though, that was all the talk after a match that had Cox questioning referee Andre Marriner and his assistants.
"Their second goal, that's when you need a referee or a linesman to spot those kind of things," said Cox.
"I don't think he (Suarez) did anything wrong. It was instinctive centre forward play.
"But if you look at the body language of players, all my lot are running to the ref and linesman and Suarez is blasting the ball in the net to say 'I've just handballed that'.
"I don't want to say anything bad about him because he is a fabulous talent, and if the shoe was on the other foot then we would have taken it.
"But when you've officials at that level, you expect them to pick up on it, but they are only human."
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Although the Mansfield fans chanted "cheat" at Suarez, Cox added: "I don't want to get involved in that. What he did was instinctive.
"We should embrace him as a talent, rather than for doing something that was instinctive.
"All he did is do what any striker would have done.
"If Matt Green had done it we would have accepted it. I can't be two faced on that."
Despite the defeat, Cox still described the last few days as "surreal" given he got married on Friday and on Sunday celebrated his 41st birthday.
The Suarez goal, though, was one that angered goalkeeper Alan Marriott, who had a close-up view.
"When you see Luis Suarez laughing as he kicks the ball over the line, he knows himself what's happened," said Marriott.
"Even Stewart Downing said to us 'I can't believe a professional official has missed that'.
"When you see that and it turns out to be the decisive goal, it's a sickener for everybody.
"But it happens. It's football, I don't think you can call him a cheat. I know a lot of people have done in the past.
"It's just a natural reaction sometimes for people to put their hand out.
"Every man, from a Sunday League football team to the Premier League is going to do that, and if it gives you an advantage and you can get away with it, then unfortunately that's football."
Despite the taunts from the fans, Rodgers has admitted to Suarez ignoring them given what he has been through since arriving in the Premier League.
"I'm not sure what anybody wants him to do in that situation," said Rodgers.
"It (the ball) hit his hand, there's no question about that, but it wasn't deliberate.
"Straightaway, even before the ball had come out of the net, I said to the fourth official 'Was that handball?'
"He said it was, but it wasn't deliberate. It's rebounded up off him."
As for the chants of "cheat", Rodgers added: "He's a thick skin. He's had it throughout his career and his life in this country as a football player.
"That's part of his life, he deals with it remarkably well, and now supporters recognise him for his qualities, which is the most important thing."