The students, who attended the Prince Edward campus of Modern College, spoke on Wednesday at the office of Hong Kong Professional Teachers' Union in Mong Kok. They wore masks to hide their identities.
Modern College said earlier that the teacher was not involved in the scandal.
The students' Chinese-language exams were cancelled because they were found copying content from the internet without giving credit in their school-based assessment projects. The project makes up 20 per cent of the subject's overall score.
When they asked their teacher - who taught three Form Six classes - if they needed to give credits to authors of original works they cited, the teacher said no.
"He said we didn't have to take the projects seriously because he wouldn't be assessing them seriously, either," said one of the four students.
The students said they did not intend to plagiarise, especially if they had known all they had to do was just to give citations.
Since the teacher-in-charge also failed to ask students to sign a declaration that their work is original and properly cited, they were suspended for violating rules set by the Hong Kong Examinations and Assessment Authority.
These students won't be able to enter university this year, but may apply next year. Students are allowed to use the better score in each subject over a two-year period. These four students will use next year's results in Chinese if they resit that part of the exam.
The students have asked the authority to reconsider its decision. "It gives a bad impression if there is a disqualification on our records and we're from Modern College," a student said. "They'll ask if we were the ones caught plagiarising."
Education sector lawmaker Ip Kin-yuen suggested that, instead of throwing out the entire exams of the four students, the other parts should still be graded, with no marks given for the school-based projects.
The school spokesman said it was still investigating the case.