What you say is not true.
Fasting is definitely a part of Krishna Janmashtami celebrations just like it is a part of the Rama Navami celebrations.
Some devotees fast the entire day & night whereas some fast only upto midnight which is the time to perform the Puja to Bala Krishna(Baby Krishna).
Some devotees break their fast by consuming the Prasadam of the above-mentioned Puja.
My reference here is the book "Essence of Dharma Sindhu" hosted by Kamakoti.org which in turn cites the Narada Purana:
In Narada Purana, Maharshi Sanatana enumerated various Vratas(religious rites) to invoke specific Deities on particular days in each month through out the year for special purposes. On the Pratipada day of Chaitra month Shukla Paksha, Shouri Vrata and Vidya Vrata are scheduled............
Krishna Janmashtami in Shravana Krishna Paksha is a very essential day for Krishna Puja when day long fasting is observed and the ten Tulasi leaf- worship is performed by reciting Krishnaya Namah, Vishnavey Namah, Anantaaya namah, Govindaya Namah Garudadhwajaaya Namah, Daamodaraaya namah, Hrishi keshaya namah, Pama naabhaya namah, Haraye Namah, and Prahavey Namah
So, as you can see, the Scriptures actually recommend a day long fast on Janmashtami contrary to what you are saying.