The former FA Cup champions lost most of their first team players, who left the club for greener pastures, leaving them 10th on the log with 19 points at the end of the first round.
"Bechem United wouldn't be part of the three clubs that will be relegated after the end of the season despite our poor form in the first round," Osei told Goal.
"We were having few issues in the beginning of first round but majority of them have been solved including the squad in-depth. The addition of new players especially strikers will solve the problems of not scoring many goals.
"It will surprise many doubters that Bechem will occupy a very respectable position after the campaign. We work with a limited budget every season but always prove a point," he added.
Bechem have signed Douglas Opoku from Great Olympics, Mpuasuman United's Daniel Afadzwu and free agent Raphael Obeng.
They will play eighth-placed Wafa in Sogakope when the league resumes next month.