The match was not facilitated on the Saturday as it would clash with Ireland's clash with France in the Six Nations at the Aviva Stadium.
Dublin chairman Andy Kettle believes an opportunity has been passed by. "I thought it was an ideal opportunity to provide the Friday night. It is a fairly decent sporting weekend," he said.
"It would give an opportunity to assess the warmth for it, how it would fit with supporters. I think supporters would react to it, people would be open to it.
"It's starting a weekend, no school the next day, quite a few work on Saturday. All that makes a difference."
Kildare chairman John McMahon said it would not be feasible for the Kildare squad to play on a Friday night given work and travel commitments.
"It was our home game and Friday night was never going to work for Kildare," he said.
"There was no official request put to us for Friday night but that would have been our decision.
"Friday night, guys trying to get home from work. It's not just a matter of getting into the car and going up the road.
"If the throw-in is 7pm, fans have to be there for 6.55pm, but the players have to be there hours before that."
It is understood that Kildare received in the region of €60,000 to play their home league games with Donegal and Dublin at GAA Headquarters.
The money will be used to upgrade the facilities at St Conleth's Park in Newbridge after the maximum capacity at the grounds was reduced to 6,000 on health and safety grounds last year.
Kildare must now convince the health and safety audit committee that a reduced capacity at St Conleth's Park in Newbridge is capable of staging league fixtures. The committee meets this week to sign off, or reject, all county grounds.
Ongoing work at St Conleth's must be completed for Kerry's visit on March 3. The ground's capacity has been reduced to 6,000, which the Kildare board agreed would not be enough to facilitate the Dublin match or Donegal on February 2, which is now a Croke Park double-header with Dublin versus Cork.
CROKE PARK Allianz League games 2013
February 2: NFL - Donegal v Kildare (5.15pm);
Dublin v Cork (7pm)
March 2: NFL - Dublin v Mayo (7pm)
March 10: NFL - Kildare v Dublin (2pm)
March 16: NHL - Dublin v Limerick (5.15pm);
NFL - Dublin v Tyrone (7pm)
March 23: NFL - Dublin v Down (7pm)