Scott Johnson's men had hoped to build on a promising display in Nelspruit earlier this year when they welcome the Springboks to Murrayfield.
But instead they handed the visitors three easy scores inside a bruising first half an hour before losing a fourth try 13 minutes after the break.
Glasgow half-back Jackson, though, insists Scotland are not as bad as the scoreline suggests.
He told Press Association Sport: "There is definitely not a 28-point margin between the teams. We showed in the summer how close we can push them.
"Today we had our chances but didn't take them. But 28 points is not a realistic representation of how close we are.
"But then again, that was how the match ended and that is what people will see.
"The scoreline was disappointing but we did play some pretty good stuff. We held onto the ball for spells but we were just not clinical enough in the important areas of the park like the Springboks were.
"They had four chances and took all four of them. That killed us off.
"To go in three tries down at half-time was very frustrating. It's always hard when you are chasing the game.
"We didn't want to go into panic mode and start throwing the ball about willy nilly. But it's tough to come back from 21 points down when you know you will have to chance your arm to get something."
Jackson was guilty of handing away possession for Willie Le Roux's try after 29 minutes as the South Africans moved 14-0 ahead.
And he was culpable once more in the second-half as he failed to find the hands of a team-mate in the move which ultimately saw the Scots driven back to their own five-yard line before Coenie Oosthuizen profited from a successful line-out drive.
The number 10 paid for that second mistake when he was replaced immediately by Warriors colleague Duncan Weir but Jackson is refusing to let his mistakes worry him.
"These things happen in games now and again," he said. "It's about learning from them and moving on.
You can't go back into your shell too much."
There is no time for the Scots to drown their sorrows with Australia awaiting them on Saturday in their final Autumn Test.
The Dark Blues registered a shock 9-6 win Down Under last year - their first in Australia since 1982 - but Jackson says they must aim to repeat that success if they want to be considered a major international power.
He said: "We don't want to be a bit-part team who scares the big sides now and again.
"We want to challenge at a consistent level and that is why yesterday was so frustrating. We didn't step up to that challenge.
"We need to take that on the chin and move on because we have only five days now before we face Australia and that is another massive Test.
"They are coming off too good wins and are full of confidence. They pose a different challenge to the one that the Boks bring.
"They play with a bit more width and put the ball through the hands a bit more so we will do our homework and make sure we are ready for them."
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