The leading wicket-takers were shock omissions for next month's tour of the West Indies when the squad was announced on Tuesday.
Strauss, who is interim managing director of England men's cricket, caretaker head coach Paul Collingwood and lead scout James Taylor made the call to discard the duo for the three Tests in the Caribbean.
"I don't think so, no," Strauss said when asked if the pair were too strong for Root to handle. "I mean, if that's the case they wouldn't have played for the last 17, 18-odd years
"It was a very hard conversation [with them]. All I can say is I hope they understood the thinking behind it and what we're trying to achieve here and also that they got the message very strongly that this isn't the end for them.
"We want them fired up and ready to go in the summer and putting their names forward for selection.
"Of course it's a high-profile decision and we know there's going to be a lot of interest in it, but we feel like we're doing it for the right reasons and this is going to help the England team to develop at a time when it really needs to develop quickly."
During Strauss' difficult conversations with the seamers, he gave no indication they were ready to call it a day in Test cricket, with Anderson having 640 scalps to his name and Broad not far behind on 537.
Strauss made a similar call regarding the pair in 2015 when they were phased out of the white-ball side following a poor World Cup campaign.
But he added: "No, I didn't get the impression from either of them that this is the end of the road or that they saw it as the end of the road for them.
"I fully expect them to prepare themselves for the summer and put their names in the frame for selection.
"When the new director of cricket and coach are appointed, hopefully they'll have more information to base their decisions going forward on what's our best bowling attack."
In addition to Broad and Anderson, England also dropped openers Rory Burns and Haseeb Hameed and number three Dawid Malan following the debacle Down Under.
Root moves up to number three
Strauss confirmed Root had asked to move up to bat at three in the West Indies.
"One of the first things that Joe Root said in the selection meeting was that he's very keen to bat three going forward," he said.
"I just feel like he wants to take responsibility and he's done that consistently with the bat over the last 18 months or so, over his entire career really.
"And he recognises that, if the top order don't lay the foundations it makes it very difficult for those coming in in the middle order, and he can help us with that."
Strauss did not give any assurances to Jos Buttler, who was one of eight from the Ashes dropped having not passed fifty in any of his last 16 Test innings.
Ben Foakes will be given the chance to stake a claim behind the stumps having lost his place in the XI after the last tour of the West Indies in 2019.
"Jos was available for selection," Strauss revealed after the wicketkeeper left Australia early with a finger injury.
"He has struggled a little bit with performance over the last 12 months or so and we've got a keeper-batter (Foakes) waiting in the wings who I think is widely acknowledged as the or one of the best keepers in the world and a very good batsman in his own right, and his record suggests that both for England and for Surrey.
"He's waited patiently in the wings and he fully deserves his chance."
With Ashley Giles, Chris Silverwood and Graham Thorpe already gone, Strauss now turns his focus to bringing in replacements and expects them to be in post by the start of the summer home series with New Zealand in June.
"That's the intention," he said. "There's a sequence to that - the director of cricket's the first appointment and then it's really important whoever that person is has the opportunity to appoint the coach or coaches that they think are most appropriate."
Collingwood could be long-term head coach
Collingwood is interim head coach for the West Indies tour and will be supported by Marcus Trescothick, Jon Lewis, Jeetan Patel and Carl Hopkinson.
Sir Andrew Strauss believes Collingwood is the right character to start England's "red-ball reset" and has opened the door for the interim head coach to hold a similar post in the future.
Strauss said: "For that tour of the West Indies, it's a five-week tour, it feels like there's a distinct advantage of having someone who has been part of that set-up already, with an established relationship with players and other support staff.
"Paul obviously deputised for Chris Silverwood out in the West Indies with the T20 team and had done a very good job out there by all accounts.
"He is definitely one we should have an eye on moving forward for a head coach role.
"It's an opportunity for him to understand what that job entails and to start this process with the red-ball reset as well. He's the right sort of character to do that.
"He's enthusiastic, he's got bundles of energy and is very clear on how he sees the England Test team playing, so it's a great opportunity for him."
Langer in contention
Events in Australia over the weekend have pushed Justin Langer high up the pecking order of candidates who could permanently replace Silverwood.
Langer resigned from his head coach role with Cricket Australia despite inflicting a 4-0 win over England months after T20 World Cup success.
But Strauss insisted his job over the coming months is merely to appoint Ashley Giles' successor after he resigned from his managing director of England men's cricket position last week.
"That's not my decision," Strauss said on Langer during his broadcast interviews.
"I have to help the ECB recruit the director of cricket and they will be thinking about the candidates for the coaching position."