The New York City firm said that the problems encountered were "normal" for a project of this scale.
"The few issues that have come up are wrinkles normal to the opening of any new building, especially when the building is receiving such a huge audience," Steven Holl Architects told Dezeen.
Hunters Point Library came under fire after its September opening because its elevator stopped short of three levels that were home to fiction books, making them off limits to visitors that are unable to walk.
Hunters Point library moves books following criticisms
The criticism prompted the library to move the books that occupied these terraced spaces to other accessible areas, as reported by Gothamist.
The inaccessibility of the three levels, however, are among a number of criticisms of the library, which cost $41 million (£31.9 million) and took over a decade to complete.
New York architecture critic Alexandra Lange took to social media to highlight that it did not include an appropriate amount of space for storing baby strollers, and that the building's one elevator was not large enough to fit them in.
"I have NEVER seen a contemporary child-focused space with enough stroller parking… that said, I am pretty shocked by the lack of communication between architect and client about many, many use issues," she said.
A parody Twitter account of the building, called Hunters Point Library, was also set up to mock the building and called attention to faults in the roof. In October, it was reported that the building's roof was leaking due to a problem with fire sprinkler and a doorway on the rooftop. Contractors were also on site to fix cracks in the floors.
However, in spite of the grumbles about faults in the design, Steven Holl Architects remains adamant that the six-storey concrete library is still proof of the value of civic spaces.
Steven Holl Architects describes project as a "success"
The library building has received 30,000 visitors since opening, according to the firm, which it says is a "testament" to its importance and success.
"The Hunters Point Library is a testament to the value of public space, and the desire of the community to have such a space to visit," said the firm. "We are pleased to see the success Hunters Point Library within the community and the city."
"The library's reading areas and study desks are continually full; people are inspired to come and spend time here," it added.
Measuring 22,000 square feet (2,044 square metres), Hunters Point Library is located on a waterfront site along the East River in the New York City borough of Queens. It is recognisable for its cast-in concrete walls painted with aluminium for a silvery finish.
Community has "celebrated the library" says firm
Huge "sculpted cuts" are carved out of the volume to form large windows with expansive views of Midtown Manhattan.
The walls are load-bearing to allow for a series of open spaces inside – including floors dedicated to children, teen and adult book collections. It is complete with a cafe on its top floor and a rooftop deck, which is yet to open.
"Not only has the local community celebrated the library with enthusiasm, but over the past month, visitorship has included a large number of young families from the wider Queens area, as well as tourists who are curious to experience the library," Steven Holl Architects said.
Photograph courtesy of Steven Holl Architects