Flintoff missed the opening encounter of the four-match series here at Lord's with an ankle injury.
But the star of last year's Ashes triumph hopes to resume as both captain and player for the second Test at his Old Trafford home ground starting on July 27, although he must first come through Lancashire's County Championship match away to Kent, commencing Tuesday.
England, in pace bowling all-rounder Flintoff's absence, never looked like bowling Pakistan out after Strauss, in his first Test as skipper, declared 30 minutes into the final day and set his opponents a Lord's record 380 to win in the fourth innings.
Strauss, whose 128 in the second innings saw him become only the third man to make a hundred on his Test debut as England captain, said: "Obviously we want Fred (Flintoff) to be fit for every Test match we play."
But opening batsman Strauss, skipper during the recent 5-0 one-day series drubbing by Sri Lanka, insisted England could win without their talisman.
"I think we can, there's definitely the raw materials there but sometimes you need to play without a player like that to learn not to rely on him," he explained after a result that left England with just two wins from their last 11 Tests.
Ian Bell is the man most likely to be dropped for Flintoff, despite the Warwickshire batsman's 100 not out in the first innings at Lord's.
"Someone is going to have to make way for Fred both as a player and as a captain," Strauss added. "I'm more than happy to support Fred when he comes back. He's done a great job for England and I'm sure he'll continue to do so."
And Pakistan coach Bob Woolmer was in no doubt about the threat posed by Flintoff. "He'll be fresh and firing," said the former England batsman. "It will be tougher for us with him in the side."
Pakistan were minus pacemen Shoaib Akhtar (ankle), Rana Naved-ul-Hasan (groin) and Mohammad Asif (elbow), as well as batsmen Shoaib Malik (elbow) and Younis Khan (knee), at Lord's.
But Woolmer insisted Younis was now "100 percent fit."
And he added that Akhtar, who arrives in England on Tuesday, would try to return for the third Test at Headingley, starting August 4, having taken 17 wickets in Pakistan's 2-0 home win over England in a three-match series late last year.
"We like to think he's in line for Headingley but there's still plenty of work for him to do. It depends on how he comes through next 10 or 15 days.
"Cardio-vascular wise he's as fit as he's ever been, we just need to get that foot right. In the end it will be up to him to tell us if he's in any pain," Woolmer explained.
By batting on Monday's final day Strauss denied an attack, where both Harmison (shin) and Hoggard (hand) looked short of overs after injuries this season, a chance of a second new ball.
Overnight, Pakistan already needed to equal the Lord's-record fourth innings winning total of 342 successfully chased by the West Indies in 1984.
But Strauss defended his decision not to declare first thing Monday on his Middlesex home ground.
"Those previous records are slightly irrelevant because the nature of the wicket here at Lord's has changed quite a lot in the last few years - it doesn't break up as much as it used to."
But Woolmer was taken aback. "If you are going to bowl a side out on the last day, you need two new balls at some stage."
The tourists, whose first innings featured a sublime 202 by man-of-the-match Mohammad Yousuf - the highest score by a Pakistan batsman in a Lord's Test - never looked like losing and closed on 214 for four second time around with Inzamam-ul-Haq 56 not out.
It was Inzamam's ninth successive fifty against England and Woolmer said of Pakistan's captain: "I thought he played absolutely brilliantly. He never looked in any trouble at all."
But that was not the case with Pakistan's novice openers, who managed just 61 runs in four innings between them at Lord's.
However, Woolmer insisted: "I think Salman Butt and Imran Farhat are good enough players to develop and get better."
Pakistan have a four-day match against Northamptonshire starting Thursday where batsman Taufeeq Umar and seamer Rao Ifitikhar Anjum, recent call-ups to an injury-hit squad, are both expected to play.
In the meantime Woolmer said Pakistan would take heart from their Lord's display. "We didn't crumble in the face or a large total, we continued the fighting spirit we've shown over the last 18 months and we are still in the series with a chance of winning."