Root admitted England were shocked to see Smith walk out to resume his innings after his sickening blow on the neck from Archer.
"It was a horrible moment. You're always trying to find different ways to get guys like Steve out but you don't want to see that. I couldn't believe he came back out but he was desperate to do well for Australia and his teammates."
Ben Stokes was man of the match for his century but paid tribute to Archer. Stokes fielded close in for most of the two Australian innings and was blown away by his impact.
"Frightening. I am not sure there will be a better debut in terms of announcing yourself in the team," he said. "The spell [to Steve Smith] was incredible to watch, we were laughing he was going to top the rankings after one test. We're lucky he's in our team. He gives you an extra dimension."
Australia captain Tim Paine was one of Archer's three second innings wickets and was clearly unsettled by his bouncers. He admitted his side will spend the next few days discussing how to face Archer.
"We have seen him for a few years now — we know the package he brings with his pace and that's something every team wants to have. It is up to us to make some new plans and get better," he said.
Root said his team "threw everything" at Australia to force a result but believes they have responded strongly to losing the first test.
The squad for the third test will be announced today and is likely to be unchanged, although England are considering tinkering the batting order again with the experiment of Root at No 3 under consideration following his first-ball duck in the second innings. Joe Denly could move to three, allowing Root back to his favourite position at four.
Jason Roy's position as opener is also up for discussion but England feel they should give him more time after years of changing their opening partnerships.