Johnson recorded career-best Test match figures of 12-127 on Saturday when the Proteas yielded tamely in the opening bout of the three-Test series.
Smith downplayed the need for video sessions or technique tweaks, saying a bouncy Centurion pitch was what made the Australian unplayable in both innings.
"I truly believe that the wicket played a big role in the success that he had," Smith said.
"He was able to extract every bit of life and uncertainty out of that wicket which, in turn, put us under an immense amount of pressure.
"Credit to him for the way he performed ... (but) I think our game plans and mindsets are good.
"It's not long ago that we can think back to big moments in games where we've been able to put him under pressure.
"The key for us now is that as a top order we set some big partnerships."
Opposing captain Michael Clarke agreed conditions played a factor in the one-sided clash.
"(Declaring after 3.2 overs on Saturday) certainly wasn't the plan when I walked out to bat today, but I saw enough in that wicket to think it was going to be quite dangerous to bat on," Clarke said.
Smith also took a swipe at the legitimacy of Johnson's recent record - 49 Test wickets at an average of 13.14 since the start of the Ashes.
"The stats, even in the Ashes, say that he picked up a lot of lower-order wickets."
Smith, though, admitted his side were comprehensively outplayed by the visitors.
He and coach Russell Domingo have just four days to sort out the side's batting, bowling and fielding woes that were exposed in the first Test.
The Proteas were held to a draw in their first Test against India at home last year, and were belted by seven wickets in the first clash of a two-Test away series against Pakistan in October.
They turned things around quickly and posted follow-up victories in both cases, and Smith pointed to the UAE series as proof of the side's self-belief.
"We've had a lot of success; we've also faced a lot of tough times," he said.
"We lost the first Test match against Pakistan in Abu Dhabi not so long ago and had the ability to bounce back.
"We were comprehensively beaten over the last four days and we've got to be man enough to admit to that and make no excuses.
"We've got to find a way to respond."
Smith suggested his side would benefit from the jarring loss, inflicted largely by Mitchell Johnson's career-best haul of 12-127.
"This side has a lot of confidence," Smith said.
"Even though it's been very disappointing, this game will benefit us going into the next game.
"Our bowlers have got good time in their legs and hopefully will be at a lot higher intensity in the next game.
"From a batting perspective, we've got some good things to talk about."