Ahead of a new accord into the higher education sector, Mr Clare said it would take at least two years for international student numbers to reach pre-pandemic levels.
He said Australia needed to be more competitive with like-minded countries in seeking out students from abroad.
"Countries like the UK and Canada are eating our lunch. When the borders were shut and when the last government told international students to go home, there was an impact," he told ABC Radio.
"International education was kneecapped by the pandemic and by those decisions, but at the same time, as numbers here were dropping, in the UK they were going up, in Canada they were going up ... we've got to do more to encourage students to come and study here."
The comments were made ahead of the Universities Australia conference in Canberra, where talks of the new accords will dominate the two-day event.
A discussion paper on the accord proposed a new long-term target for higher eduction and participation.
The current measure of bachelor degree attainment for people aged 25 to 34 is 44.6 per cent - above the average for OECD countries of 41.5 per cent.
But it lags behind the highest achieving countries such as the Netherlands (54.3 per cent), Switzerland (52.3 per cent) and the UK (51.2 per cent).
This is despite increases in graduate numbers over the past two decades, the paper says.
Seeking a higher attainment target will also drive universities to lift the proportion of students from under-represented groups, the paper argues.
In 2021, 17 per cent of higher education students were from a low socio-economic background, 2.4 per cent were Indigenous Australians, 21 per cent were from regional or remote areas, and nine per cent were students with a disability.
"Almost 50 per cent of young people have a university degree today, but only 20 per cent of Aussies from poor families, only 20 per cent of Australians from the regions and only seven per cent of Australians from an Indigenous background," Mr Clare said.
"You can't fix this all at the university gate, but you can do some real things here, but it's got to go back further into the school system and even further back than that into our early education system."
The accord panel will present an interim report to the minister in June and a final document in December.
Mr Clare said it was likely there would be some form of higher education reform in next year's federal budget, following the report being handed down.
"Next year's really going to be the start of implementation, but what I'm encouraging the accord team to think about is ... what do we need to do now, what do we need to do next year, where do we need to be by 2030?" he said.
Universities Australia chief executive Catriona Jackson, who will deliver the welcome address, said the accord was the "biggest opportunity for policy reform in our sector in decades".
Australian universities educate 1.5 million students each year, as well as employ hundreds of thousands of people and produce world-class research and development.
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