The hosts finished eight runs short of a world record target of 458 as they cautiously played out the final three overs at the Wanderers on Sunday, settling for a draw with three wickets in hand.
Victory would have comfortably eclipsed the current world record of 418 runs chased down by West Indies against Australia in Antigua in 2003.
Steyn was at the crease with Vernon Philander and was seen instructing his batting partner to be cautious, which led to the duo being booed off the field by their own supporters despite salvaging an excellent draw from a game that India dominated for the first four days.
"Dale was really upset, he struggled to handle it," AB de Villiers, who leads the team in limited-overs matches, told reporters.
"It really took Graeme (Smith) and a few guys to help him handle it immediately, because of the crowds, the booing and everyone criticising him and Vernon (Philander).
"They took a lot of strain and it was up to the team to pull through that but it was really tough."
De Villiers, who made 103 in a 205-run stand with Du Plessis (134) to set up the chance for an unlikely victory, reassured Steyn that he made the right decision.
"A lot of people are blaming Dale and Vernon but I honestly believe that the numbers nine, 10, 11 should never be going for the runs. It's up to the top six to score the runs," he said.
"If responsibility is going to be thrown around, it's on me, Faf (du Plessis) and JP (Duminy) and maybe a little bit on Vern at the end there.
"The minute Dale walked to the crease, the right thing to do was to save the test match and I thought they did that brilliantly well."
De Villiers said captain Smith and coach Russell Domingo have stressed on the achievement of the draw after South Africa made 450 for seven in the second innings on a wearing pitch, the third highest fourth innings total in the history of the game.
"At the end, we had a really good team chat, where Russell and Graeme spoke really wise words and I think the whole team is in a good space after that," the wicketkeeper-batsman added.
"We pulled up an amazing draw and those were Graeme's words. It was about just how amazing a team we are and what we've achieved over the last while.
"That we should not go down with the criticism we will get, but to remember that we are a team of character and to keep believing in ourselves and our team-mates.
"That's why we play the game - for each other. So we look each other in the eye and we are really chuffed with a great draw."
The second test of the two-match series starts in Durban on Thursday.