Arthur described the tourists as "predictable" following the second Twenty20 international last week, while he called the decision to bowl Adil Rashid for only one over in the same game as "criminal".
Speaking ahead of the first of five one-day games in Johannesburg, he said: "At the end of the day, we were just being honest with the media. I don't think we did it with the intention of playing any sort of mind games.
"It does happen in world cricket and there are times when you want to create a subtle message, perhaps put a little bit of doubt into the opposition camp, and if we've done that, great. If we haven't, then it's not a problem.
"We don't go in with any deliberate policy to undermine anybody in the opposition camp.
"We respect England hugely, we respect the opposition hugely, so it just depends how they take it, that's all."
There has been more spice added to the Rashid debate after the visitors called James Tredwell into the squad as cover for injured slow bowler Graeme Swann.
Arthur, who felt England had showed a lack of confidence in the Yorkshire leg-spinner last week, was asked who he thought would play on Friday, and responded by saying: "I think Adil Rashid will play. It clearly makes sense that he'll play.
"He was their second-choice spinner. It will be up to them but it will be strange if they went above Adil Rashid again."
Fletcher involved againAnother dimension to the series is the employment of former England coach Duncan Fletcher by South Africa in a consultancy role.
The Zimbabwean led the tourists in a fruitful spell between 1999 and 2007, which included the famous Ashes victory of 2005, and Arthur revealed they would use his inside knowledge to aid their cause over the next two months, with four Test matches also on the agenda.
"I think he was very highly respected by a lot of their players, some of whom are still playing," continued the Proteas' coach.
"Probably, at the back of their minds, they may be thinking, 'I wonder what sort of information he's given out'.
"At the end of the day, he is going to be with us for a short period of time and we need to maximise that time in getting an insight into England."
There is, of course, plenty of hype heading into the opening game, more so if England's recent record against South Africa is taken into account - they have won the last five meetings, including a famous victory in September's Champions Trophy that dumped their opponents out of the competition on home soil.
"England are a very strong unit, there's no doubt about it, and we know we've got to play our 'A' game to beat them," added Arthur, who addressed the media after captain Graeme Smith was excused due to family reasons.
"I think England are a very, very good team. They are a work in progress but they've got some really good players who on their day can win games. So we're very wary of them and know it's going to be a tough series."
Smith is expected to lead the side but vice-captain Johan Botha, Wayne Parnell and Hashim Amla missed out on the final 12-man squad.
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