Alexander’s comments were made in a statement submitted to Holyrood’s education committee.
Gillespie resigned with immediate effect in December after telling staff the previous month that job losses were “inevitable”.
He is expected to give evidence in person at the committee on Thursday.
The university currently faces a 拢35m deficit and has said it must cut 300 jobs through a voluntary redundancy scheme.
The independent report, published last week, said university bosses and its governing body failed multiple times to identify the worsening crisis and continued to overspend instead of taking action.
In her statement, former Labour MSP Alexander said: “I personally, was progressively frozen out of meetings, my objectives changed, data withheld and when I challenged the absence/adequacy of financial information in Sept (20)24, I was then asked to leave.
“I declined the offer of overseas trips at the university’s expense to be followed by a generous settlement payment.
“Quite simply, it seemed unethical and morally wrong.”
Alexander, who now sits as a baroness at the House of Lords, said she felt “punished for speaking out” and that the university “failed to fix the roof when the sun shone”.