Dominic Shellard, the De Montfort University vice-chancellor, said the institution had received "hundreds and hundreds" of queries from "very distressed" students.
Some students have been unable to accept offers via the University and Colleges Admissions Service's Track system, which allows them to monitor the progress of their applications.
Web-link, the Ucas system which allows universities to keep track of applicant data, has also been affected.
Professor Shellard highlighted the difficulties this caused for universities in hitting their targets for student numbers. Universities face significant fines if they over-recruit students.
"It is utterly infuriating that having spent many months planning...in terms of bringing admissions in line with student numbers controls, we are flying blind at the moment," Professor Shellard said.
The government and the Higher Education Funding Council for England are yet to notify institutions about the level of over-recruitment fines, but they are expected to rise to around £10,000 a student.
Professor Shellard said the problems introduced "a completely unnecessary further element of chance into a process that was already very challenging in terms of fines".
He added: "I bitterly regret the huge additional distress that has been caused to students up and down the country."
Professor Shellard said De Montfort had planned to recruit 400 students via clearing. As of 5pm yesterday, it had made 320 offers but "only four students had accepted according to the Ucas website", he added.
A Ucas spokesman said systems had been "extremely busy" yesterday causing slow running during the day.
"Universities and colleges were unable to process decisions for around three hours in the afternoon and for a short period in the evening. There were two separate systems issues at play and both were resolved," he said.
"This did cause some regrettable disruption for admission offices and some applicants couldn't check updates on their status following verbal offers.
"We were able to process data coming to us from the universities and colleges during the evening and overnight and started the day today up-to-date in terms of showing decisions and vacancies.
"We do anticipate another busy day today. Systems have been running well since yesterday evening and are fully operational."
But Professor Shellard said there "clearly" were "massive problems with Ucas" and said he thought the issues were ongoing today.
Ucas had been advising students yesterday that "it is not really a problem, it is just volume of traffic", Professor Shellard said.
He added: "Whilst I fully accept that systems can go down, I'm sure the Ucas board will want to reflect on the transparency of their [Ucas'] communication."
The Ucas board is chaired by David Eastwood, vice-chancellor of the University of Birmingham.