More than a third of results were lower than previously estimated after they were calculated using a standardisation method.
Exams were cancelled due to coronavirus restrictions.
Stormont education minister Peter Weir said official procedures were robust and the outcome more equitable for all students.
Lagan College principal Amanda McNamee felt “disappointed and embarrassed”.
She said: “They are real children with real lives, they aren’t computers, they are not data, not anomalies, and I feel we have let them down.”
Northern Ireland’s exams board has said there will be some “anomalies”.
The school head told the BBC: “If I hear the word anomaly again being linked to an actual real person, a real child, I think I am going to scream.”
In 37% of cases teachers were over-optimistic in their prediction, while in around 5% of tests they underestimated the result, statistics published by the education authorities on Thursday showed.
Exams body CCEA (Council for the Curriculum, Examinations and Assessment) chief executive Justin Edwards defended its standardisation model for grading.
He said: “All of us at CCEA, working closely with the education community, have strived to ensure that students are able to progress this year.
“As a result of this collaborative work, we have delivered grades to students which we predict they would have achieved had they sat the examinations and which carry the same value as in previous years.
“Northern Ireland students have seen slight increases across grades, which are comparable with previous year-on-year performance for this particular year group.”
This is a difficult day for many young people receiving A-Level results.
The situation that many students find themselves in is unacceptable.
There needs to be an urgent resolution.
A-Levels will be discussed at the Executive & I will urge Education Minister to fix this wrong pic.twitter.com/sxXXsyG0S3Advertisement— Michelle O’Neill (@moneillsf) August 13, 2020
Stormont deputy first minister Michelle O’Neill said it was a difficult day for many young people.
“The situation that many students find themselves in is unacceptable.
“There needs to be an urgent resolution.”
The calculation saw pupil performance increase across all grades relative to previous years.
The overall pass rate of pupils achieving an A*-E grade rose by 0.8 of a percentage point to 99.1%.
Pupils achieving the top A* grade increased by one percentage point to 9.8%, while those achieving A* or A grades rose by 2.3 percentage points to 33.2%.
Female students again outperformed male counterparts at the highest grades, with the gap broadly in line with recent years.
The calculated system also saw performance at AS level improve on 2019.
The percentage attaining a top A grade rose by 2.1 percentage points to 29.4%.
Those attaining an A-E grade rose by 0.9 of a percentage point to 96.4%.
Data indicated that the increases in attainment would have been significantly higher if the predicted grades assessed by teachers were used without standardisation.
Teachers are asked to predict grades every year in Northern Ireland as part of normal assessment procedures.
In 2019, around 46% of grades match the results attained by pupils and 40% proved overly-optimistic.
The CCEA standardisation model asked teachers to give a predicted grade for their pupils and then rank them in order within their class.
The exams body then used other data to standardise the results.
For A-levels, the CCEA model used pupils’ AS level results, making adjustments for those who had applied to take resits.
For AS results, the pupils’ GCSE results were used, as was the performance by their school over the previous three years.
