Flintoff bowled only 11 overs on the final day as Australia - in trouble at 161 for four before lunch - batted on and on to reach 375 for five before the two teams shook hands on a draw, reports The Independent.
"He seems OK," insisted Strauss. "It was one of those situations towards the end where I'm conscious there is no point in tearing him to death when there's not a lot going on. But I think he is doing OK and we are still very confident he will be OK for Headingley.
"There is obviously some soreness but I don't think anything has deteriorated massively. He needs to rest up well because back-to-back Tests are hard for any bowler. Then we will see how he is on Thursday," he added.
Flintoff, who has had injections between Tests to keep him going, insisted on Sunday night that it would take something "pretty serious" to force him out of the action at Headingley. And with England still one up, he knows that a victory in Leeds will see the Ashes regained with a match to spare.
"If he's not fit enough to do the job he won't play. But if he is fit, we want to play him. The Headingley Test is a massive Test - if we win there, then we win the Ashes," Strauss added.
"He will be assessed this week and he knows what to do with the injury but the key is how sore he is on Thursday. Fred has to be honest about his body and he has been so far," Strauss said.
Strauss also admitted that England were bullish yesterday morning about their chances of going 2-0 up at Edgbaston.
"We came to the ground optimistic that we might be able to force a result, so it's a little bit of a let-down," he said.
"But the conditions didn't help us like we thought they would and the ball didn't swing. But there are still a huge number of positives to come out of the game and for three days we were on top of Australia again," he added.
England's last hope of success yesterday came when Strauss dropped Michael Clarke on 38 in mid-afternoon off the bowling of Ravi Bopara. Clarke went on to hit an unbeaten century - his second hundred of the series - and he shared in a match-saving stand of 185 with Marcus North.
"If I'd caught that you never know but we were getting to last throw of the dice time," said Strauss.