In a battle between the world's top two teams, and with England's number one ranking on the line, Strauss had expected his men to flourish in the familiar conditions but instead floundered as South Africa dominated the contest to go 1-0 up in the three-match series.
"Most of my regrets are that we did not come out with a draw," Strauss said. "We should have done that."
Strauss especially rued how England lost wickets at times in the match when he thought they could have done better like on Friday morning when they plummeted from their overnight 267 for three to 385 all out.
In the second innings on Sunday, England lost four key batsmen to close 102 for four, en route to being 240 all out.
South Africa had far less trouble on a placid batting surface at The Oval, as they posted a huge total of 637 for two. Hashim Amla broke the national batting record with 311 not out.
"Losing four wickets last night was a body blow for us," said Strauss.
"The South Africans did get it reversing today and with more wickets in hand we could have batted out the day.
"There are a number of areas where we are frustrated. We did not deal better with those conditions and losing four wickets last night in placid conditions made life difficult for us today. There are regrets there but we will learn the lessons and come back strong next week."
The teams meet again in Leeds on August 2, before the final clash at Lord's on August 16. Strauss was keen not to panic by the defeat and said he still had faith in his team, especially the batsmen, who have flourished in home conditions for a long period of time.
In contrast, the tourists played an almost perfect game of test cricket. But coach Gary Kirsten wanted to remain level-headed with two games still to play.
"We've got a long way to go," he said, in the absence of captain Graeme Smith, who had left for the airport to return home for the birth of his first child.
"We've put our peg in the ground, we want to become the best cricket team in the world and we know what we need to do to be able to achieve that. This is just one part of the process. We had a good tour of New Zealand and achieved what we wanted to achieve there, and this is the next hurdle.
"We are 30 per cent of the way through the test series; there is a lot of work to be done; there is a lot of focus needed, we literally take each day as it comes."