England collapsed in the second innings to 149 all out having started the second innings requiring 161 runs to take the game into the fourth innings.
Despite previously chasing down high totals with relative ease earlier in the summer - including 378 to beat India - England slumped and were unable to take the game even into the evening session on the third day.
It was the first loss England have suffered since Stokes and Brendon McCullum were appointed following a dismal winter and a run of just one win in 17 Test matches.
However, despite the result and performance at the home of cricket, there is a clear message from Stokes instilled in the team through the aggressive so-called "Bazball" approach.
The teams meet again in the second Test at Old Trafford, starting in Manchester on Thursday, and the England captain said: "Everyone's so aligned in the dressing room, from the management to the players, about how we operate.
"Captains and coaches are always going to get criticised. (It's) part and parcel of doing this role.
"We've got a certain way we want to play. We know we can be an incredibly hard team to play against if we execute that, hard to beat.
"We can't be great every day. This week was just off for us. But we're not going to hold on to it for too long and carry any baggage to Manchester."
England struggled to weather the storm, especially from South Africa's pace attack as Anrich Nortje's blistering pace proved too much for the England middle order as he claimed three wickets in just 10 deliveries during the afternoon session.
However, Stokes insisted England do have to absorb pressure at times and will not just go all-out in terms of playing attacking cricket.
"Not only do we speak about wanting to put pressure on to the opposition, but there are going to be times when we need to absorb that pressure, and I felt we were absorbing a lot of pressure this week because of how South Africa bowled - especially those spells from Nortje and Rabada on day one," he said.
"When we do have to absorb, we try to do it in a positive way, but the way they bowled… they were just relentless.
"You have to hold your hands up sometimes. When you're playing international sport, some days they're going to be better than you, which is fine."