"I've always got on with Kevin," Strauss told Sky Sports after Pietersen was excluded from the squad for the third and final Test against the Proteas starting at Lord's on Thursday.
"I've tried to be honest with him; he's been honest with me.
"That's why this has all been a bit of a surprise to me.
"I think the discontent that Kevin had with the (England and Wales Cricket) Board over his contract situation was one that the players didn't get involved in - and I didn't really get involved in, if I'm honest.
"But over the last week I have had to get involved, because there have been issues a little bit more central to his relationship with the other players and our ability to perform out in the middle."
Pietersen had intimated after the second Test that he intended to retire altogether from international cricket, only to issue a statement via a staged YouTube interview insisting he was still committed to playing for England.
As Pietersen seeks to talk his way back into the England fold, Alec Stewart, executive director at the batsman's county Surrey, told the BBC he had heard the player had said sorry to the England and Wales Cricket Board over the texts episode.
"I'm hearing he's now apologised but hasn't had any confirmation back from the ECB," said the former England captain.
South Africa all-rounder Jacques Kallis believes England will miss Pietersen.
"He's a world-class player and he's proven that over many years - putting in big performances for England - so I'm sure he's going to be missed," Kallis told Sky Sports.
"I don't think it will affect him, I think he'll bounce back and I think he's still got a lot of cricket ahead of him. He's too good a player to stay out of the international scene."
But Graeme Swann and Tim Bresnan said England would work better as a team without Pietersen in a match they must win to ensure they remain the world's number one Test nation.
"Just because you lose one player it doesn't necessarily make you a weaker team," said England off-spinner Swann in his Sun newspaper column on Tuesday.
"We all need to be pulling in the same direction - not 10 of us doing it and one of us not."
Swann said England's one-day results had improved since Pietersen gave up 50-over and Twenty20 international cricket in May. "Since Kevin retired from limited-overs cricket we are unbeaten in all matches in the shorter formats," he said.
England paceman Bresnan said: "It may be an even better side.
"It's one of those things where a talented player has been replaced by another talented player. Why should we miss certain individuals just because they're not available for selection?"
Jonny Bairstow will replace Pietersen at Lord's.
Pietersen, man of the match at Headingley for his 149 in the second Test, was dropped for the final Test the day after his YouTube interview because of the controversial text messages.
Bresnan said the spirit among the squad, who are 1-0 down in the series, had not been destabilised by the furore surrounding England's most explosive batsman.
"We met up yesterday, the mood in the camp was exceptional. It's just like it always is. Always relaxed, quite focused, but we've always got the driving desire to get that win," he said.
The Lord's Test starts on Thursday.
In another twist to the embarrassing saga, England paceman Stuart Broad issued a statement on the ECB website denying any involvement in a fake Twitter account using Pietersen's name.
Broad said: "Following last night's statement by Mr Richard Bailey that he was responsible for creating a fake Twitter account in Kevin Pietersen's name, I would like to confirm that I had no involvement in this whatsoever.
"I met with the Managing Director - England Cricket, Hugh Morris, this morning and assured him that I did not play any role in the creation of this account or provide Mr Bailey with any information regarding Kevin Pietersen or the England team.
"As has been widely reported Mr Bailey is a friend of mine, but we had no conversations regarding this issue at all and I am pleased that he has now decided to close the fake account down."
Morris told the website he was "fully satisfied" Broad had not breached the confidence of any of his England team-mates.