Cox, though, was left "gutted" for the club and his players at the 59th-minute incident that clinched the 2-1 win for Liverpool's at the non-league Stags' expense.
Debutant Daniel Sturridge, a £12million buy from Chelsea in the past few days, set the Reds on their way to the win with an eighth-minute strike.
As Liverpool boss Brendan Rodgers pointed out after the game, his side should have been "out of sight" before the introduction of Suarez as a replacement for Sturridge four minutes prior to his controversial goal.
Matt Green gave the Blue Square Bet Premier side hope 11 minutes from time, but it was not to be – leaving Liverpool to travel to npower League One side Oldham in the last 32 of the tournament.
Suarez, though, was the main talking point post-match after an encounter 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 into 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 have officials at that level you expect them to pick up on it.
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. He did 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 that he got married on Friday and yesterday celebrated his 41st birthday.
The Suarez goal, though, was one that angered goalkeeper Alan Marriott, who had a close-up view. He said: "When you see Luis Suarez laughing as he kicks the ball over the line, he knows himself what's happened. Even Stewart Downing said '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. A lot of people have done it in the past.
Meanwhile, Arsenal and Swansea will be preparing for a third-round replay after a 2-2 draw at the Liberty Stadium.
Fourth round draw: Norwich v Luton, Oldham v Liverpool, Macclesfield v Wigan or Bournemouth, Derby v Blackburn, Hull or Leyton Orient v Barnsley, Middlesbrough v Aldershot, Millwall v Aston Villa, Leeds or Birmingham v Tottenham, Brighton v Swansea or Arsenal, Crystal Palace or Stoke v Manchester City, West Ham or Manchester United v Fulham or Blackpool, Southend or Brentford v Chelsea, Reading v Sheffield United, Huddersfield v Leicester, QPR or West Brom v Sheffield Wed or MK Dons, Bolton or Sunderland v Cheltenham or Everton. Ties to be played on January 26-27.
TONIGHT: Third round: Cheltenham v Everton (7.45).