Ronaldo was clearly frustrated after his team's campaign got off to a stumbling start in Group F. At full-time remonstrated with the referee and only shook the hand of only one Iceland player.
Five minutes before full-time he had missed a free header that would have won Portugal the game.
Arnason added: 'He's a fantastic footballer but he's not a gracious human being and the thing is we almost nicked the win so him saying we weren't going for the win contradicts that.
'We got a draw and could have nicked it. Obviously we're not going to create as much chances as a fantastic team like Portugal but his comments are the reason why [Lionel] Messi is always going to be one step ahead of him.'
Former Chelsea and Bolton forward Eidur Gudjohnsen - an unused substitute - said: 'Drawing, for us, has been marvellous.
'We don't concentrate on the other teams. Our performance was one of pride, character and, above all, hard work. I don't really care what Ronaldo has to say.
'He said we were lucky but you always need luck. Luck doesn't fall from the sky, you have to earn it.'
Defender Arnason enjoyed a good evening up against the twin threat of Ronaldo and Nani, who scored Portugal's goal in the first half.
He will probably never the forget the night he and Malmo were humbled by Ronaldo, who hit four goals.
'We didn't have the strongest team at the Bernabeu, it doesn't compare to what we have here,' he said.
'This is better organisation, much better players and when it's like that it's a bit easier.
'But that night was horrendous. It was a poorly set-up game and we gave it to them on a silver platter. We didn't even make it hard for them.
'Today we didn't really touch the ball but we got a good result. Me and Ragnar don't let many chances in and with the goalkeeper we have here we always trust he's going to mop up what's left.
'We're taking it one game at a time as always. We're an underdog going into every game and it suits us perfectly.
'We've got a solid team. A team that's willing to work for each other.'
