The soul legend was scheduled to perform at Houston's service in New Jersey, but declined to appear due to "terrible leg spasms and locked muscles".
Franklin did, however, perform a concert at the Radio City Music Hall in New York that evening, where she spoke lovingly of her late goddaughter.
"I hope that there's something I will sing, or I have sung, that will lift all of our heavy hearts today," WENN quotes her as telling the audience.
The 69-year-old later performed a cover of Houston's famous track 'I Will Always Love You' and said: "She was a very fine young lady... one of the best, greatest singers.
"She was giving, gave so much of herself… God bless you, Nippy. We'll always remember."
Franklin claimed shortly after Houston's death on February 11 that the star had tremendous trouble dealing with fame.
More Whitney Houston coverage:
> Whitney Houston 1963-2012: Reactions
> Whitney Houston 1963-2012: Obituary
> Whitney Houston: A life in pictures
> Whitney Houston: Greatest musical achievements - pictures
> Whitney Houston to dominate singles, album charts next week
> Bobby Brown: "I love you, Whitney"
Click through a gallery of Whitney Houston's life below: