Under a Scottish Government initiative to get more bright pupils from deprived backgrounds into higher education universities were given 727 extra funded places this year.
However, figures show Aberdeen University was unable to fill any of the additional 75 access places it was allocated.
Overall, however, Scottish universities have made good progress under the initiative, with some 80% of the total places filled.
St Andrews University, in Fife, which has been criticised for its failure to widen access in the past, filled all of its 20 extra places.
Glasgow University recruited the most students from the 40% of poorest postcode areas, with 175 signed up from a total target of 200.
The higher education sector has also been successful at filling the 1020 extra places allocated under a separate route to encourage college students into a degree course - so-called articulation - with some 98% of the total reached.
A spokeswoman for Aberdeen University said 140 students from the poorest postcodes had been recruited this year and every effort had been made to fill the extra places.
She said: "Our university draws almost half its annual intake from Aberdeen City and Aberdeenshire, where there is a lower number of the most deprived postcodes compared to other areas of Scotland.
"We are working with the Scottish Funding Council to widen the set of metrics we use to measure widening participation, to support our outreach to individuals from challenged backgrounds who live outside the specific neighbourhoods identified in the Scottish Index of Multiple Deprivation."
The overall performance was welcomed by student representatives and the university sector.
Gordon Maloney, president of NUS Scotland, said: "These figures offer some very positive signs that efforts to improve fair access are working. There are still some institutions that can clearly do better, with Aberdeen University in particular standing out, but there's some great work going on right across institutions in Scotland."
Alastair Sim, director of Universities Scotland, which represents university principals, said universities had worked very hard to fill the extra places.
He said: "This means over 1600 students, living in the most deprived parts of Scotland, have started university this autumn or will be coming straight from college in a year or two's time who might not otherwise have had the chance."
Mr Sim said that because it was the first year of the scheme - with the extra places announced mid-way through the application process - it was understandable that not every one had been filled.
He also suggested that, given Aberdeen University's figures, that using the poorest postcode areas as a measure was not appropriate for all parts of Scotland.
Laurence Howells, interim chief executive of the Scottish Funding Council, which administers the scheme on behalf of the Scottish Government, said he was pleased with the progress.
He said: "Universities have responded very positively to this pioneering initiative. Next year, with a longer recruitment cycle, even more students will benefit.
"What's especially good is that these are all additional places added into the system for the first time so around 600 talented students from poorer areas now beginning their university education. That's a great result."
Currently, the middle classes dominate higher education and access initiatives have only gone a small way to redress the balance.
The Scottish Government has made it a priority for universities to improve rates of participation by pupils from deprived backgrounds after a decade of stagnation.
All institutions have been tasked with improving access under new outcome agreements with the Scottish Funding Council, with those that fail facing a funds reduction. The Government also provided £3.5 million of funding to pay for extra places to kick-start the initiative.