First Minister Nicola Sturgeon has said any "genuine individual injustices" over exam results will be "rectified" through the appeals process.
There was criticism after thousands of students received lower grades than had been estimated by their teachers.
Ms Sturgeon said she understood the "anger and upset" felt by young people.
She encouraged those feeling aggrieved to lodge appeals, which would be based on "individual merit" rather than "statistical moderation".
Scottish students received the results for their Nationals, Highers and Advanced Higher courses on Tuesday.
After exams were cancelled due to the coronavirus pandemic, teachers were asked to estimate a grade for each pupil.
These results were moderated by the Scottish Qualifications Authority (SQA), which led to 125,000 estimated grades being lowered - a quarter of the total.
Some pupils whose results were lower than expected believe that the moderation process penalised schools in less affluent areas.
The Higher pass rate for pupils from the most deprived backgrounds was reduced by 15.2 percentage points from teachers' estimates, compared to 6.9 percentage points for the wealthiest pupils.
Education Secretary John Swinney has denied that bright pupils from deprived areas were unfairly penalised.
Some pupils are planning to stage a protest in Glasgow's George Square on Friday.
Asked at her daily briefing if she would have joined the protest if her own results had been downgraded because of her school's historic standards, Ms Sturgeon said it was "very possible".
"If I had been in that position, I would feel aggrieved about that," she said.
"I totally understand, and sympathise and empathise, with any young person who is in the position of having a grade awarded by the SQA that is lower than the teacher estimate for that grade."
How will the appeals process work?
There is a free appeals process for students who received a lower grade than was originally estimated by their teacher or lecturer.
The appeal must include alternative evidence, and should be submitted by the school or college rather than the candidate. It is only possible to review a grade, not a band.
Priority reviews - for those pupils who have a conditional offer for university or college - must be submitted by 14 August. The deadline for all other appeals is 21 August.
The SQA says that the alternative evidence which can be submitted can include any completed coursework which had already been sent to the SQA, as well as coursework which could not be completed.
It can also include prelims or mock tests, class work and commercially-produced question papers - but not past papers which were in the public domain.
Grades can either be increased, lowered or remain the same.
The first minister said the moderation of results had been necessary to "command the confidence of colleges and universities and employers".
She said that whichever way results were calculated this year, some people would have felt the system was not fair.
Ms Sturgeon urged pupils to lodge appeals if they felt there had been "genuine individual injustices".
She said that rather than being based on statistical moderation, the appeals would be based on a candidate's individual merit.
"This next part of the process is very much about making sure that individual cases of genuine unfairness can be rectified," she said.
"That is why we would encourage all young people who feel that they have not had fair results to go through this appeal process."
The Scottish Conservative Party's new leader, Douglas Ross MP, said pupils should be allowed to choose between the result they received on Tuesday, their prelim result, or sitting exams this autumn.
"It is only fair that pupils are given every single chance to succeed," he said.
"We should allow pupils far more flexibility and give all pupils - no matter their background - every opportunity to get the grades they deserve."
The Scottish Greens have called for a "no detriment" policy in the appeals process, where no-one would be given a grade lower than they achieved in their prelim.