The paper apologised for "insensitive language" in its report that linked the accident to previous "drunken partying and the wrecking of apartments".
Five of the six people who died were Irish students temporarily in the US as part of a work exchange programme.
In a letter, Mrs McAleese said the report used "lazy tabloid stereotype".
She said she had been part of the same visa programme more than 40 years ago and out of tens of thousands of students who had visited the US, "the vast majority have been a credit to Ireland".
In the letter published by the Irish Times, Mrs McAleese said the report had "heaped deliberate injustice on top of the most awful grief".
The newspaper said in a blog that the article was intended to explain in greater detail why the young Irish students were in the US, and many of the complaints it had received were valid.
New York Times spokesperson Eileen Murphy said in an email: "It was never our intention to blame the victims and we apologise if the piece left that impression."
Read more: Tributes to Berkeley balcony victims
The incident happened during a 21st birthday party in the early hours of Tuesday in the city of Berkeley.
Engineers say water damage may have caused the structure to give way.
An initial investigation found that the balcony support's wooden beams may not have been sealed properly at the time of construction, Berkeley Mayor Tom Bates said.
However, he later stressed that this was not an official conclusion and that an investigation was still under way.
Authorities said 13 people were on the fourth-floor balcony when it collapsed.
People left flowers and other tributes at the scene on Wednesday as flags on both sides of the Atlantic flew at half-mast.
Irish students held a candlelit vigil in a park close to the scene of the tragedy on Wednesday evening, and a memorial church service was held in Oakland.

Only 1,338 spectators turned up for the EFL Trophy second-round tie against Crawley Town, which they won 1-0.
League gates have already dipped this season, with an average attendance more than 3,000 down on last season.
Sky Blues fans are unhappy at the way their club is run by owners Sisu.
Only one and a half stands were open at the 32,609-capacity stadium for the game against Crawley, with just 57 away fans making the trip.
The crowd was lower even than the 1,603 who watched City's game against Carlisle United in February 2014, during their season at Sixfields, Northampton - the club's previous lowest ever 'home' crowd.
Although attendance figures initially rose when City left Highfield Road for the Ricoh Arena in 2005, interest in the club has been decreasing steadily over the past decade, especially since relegation to League One in 2012.
The Sky Blues are in their fifth campaign in the third tier of English football - and only once has their average seasonal attendance increased in that time - last term's relatively successful campaign, when they briefly led League One under Tony Mowbray before falling away to finish eighth.
Under interim manager Mark Venus, they are currently in the relegation zone, in 21st place, after four straight league defeats.
Relegation would take the club to their lowest place in the Football League since winning promotion from the old Division Four in 1959.
City fans, who boycotted home games in the year at Northampton, have become increasingly dispirited this season.
At the recent home fixture against MK Dons, they staged a mock funeral procession "in affectionate remembrance of Coventry City Football Club which is dying due to neglect and abuse at the hands of Sisu from 2007 to 2016".
They also joined in with equally disaffected Charlton Athletic supporters in the joint 'pigs might fly' pitch protest in the away match at The Valley in October.
Coventry have had some success in the Football League Trophy, reaching the two-leg Northern final in 2012-13, before going out in the Southern semis in 2014-15.
However, there appears to be less interest generally in this season's revamped competition, and Coventry's two previous home ties this season each attracted just over 2,000 fans.
But prior to this season, City's average home attendance in the Trophy was 12,284.
2012-13: Beaten Northern section finalists
2013-14: Knocked out in second round (no home tie)
2014-15: Beaten Southern section semi-finalists
2015-16: Knocked out in second round (no home tie)
2016-17: Last 16
The New York Times "should be hanging its head in shame" over a report on the California balcony collapse, former Irish President Mary McAleese has said.
[NEXT_CONCEPT]
Struggling Coventry City's off-field problems were further highlighted at the Ricoh Arena on Wednesday night as they attracted their lowest-ever crowd for a first-team game.