Smith has made his return to the famous English ground this week, training on Saturday for the first time since the first Test. Australia's players did not enter the centre wicket, but Wednesday's second Test at Lord's will mark Smith's first match back there since the 2019 Ashes.
He briefly returned to the field at the fall of the next wicket before being out lbw for 88. He was subsequently ruled out of the match with concussion.
"It was a very difficult period to get through," Smith told the Legend of the Ashes podcast. "I caught one on the arm, got away with a few pull shots that are top edge and a couple in the gaps.
"And then I copped one in the back of the head, which hurt a fair bit. At that stage, I didn't realise I was getting concussed. I went off and did all the tests, passed all the tests.
"It wasn't until I came back out. Half-an-hour after, when the adrenalin sort of went out of my system and I started to feel quite groggy - probably like I'd had a dozen beers, to be honest."
Smith also revealed he had difficulty picking up the ball that day in the rain-affected drawn Test. "It was quite a dark, gloomy day. The clouds were rolling in and out," Smith said.
"Lord's itself can be a little difficult when they are bowling from the members' end with the members sitting there and the sightscreen not as big as at other grounds.
"There were a few distractions there, and it was just a day [when] I wasn't quite seeing the ball as well as I would have liked from that end."
The fact Archer is missing this series through a recurring elbow injury is one of the great disappointments of the English summer, such was the ferocity of the pair's battle in 2019.
Smith's exit from that Lord's match prompted the rebirth of Marnus Labuschagne as a Test batter, brought back into the Australian side and averaging 59.34 since.
As a result of the concussion, Smith did not play in Australia's Headingley demise in the next Test but returned for the final two matches and finished the series with 774 runs at 110.57.