Near as I can tell, these are the Number One pop hits in America, beginning with the advent of the British Invasion and its first Number One hit, the Tornados' "Telstar," at the tail end of 1962, that did not include the title phrase in the song's lyrics (instrumentals not included) (I have also omitted songs where the title phrase is an abridgment of the song's lyrics, such as the Righteous Brothers' "[You're My] Soul and Inspiration," wherein they do actually sing "You're my soul and... inspiration") :
"Sukiyaki" by Kyu Sakamoto (went to Number One in June 1963): It's in Japanese, but I'm reasonably certain that Kyu never says "Sukiyaki," since that title was appended to the song by a Capitol label exec
"Fingertips (Part 2)" by Little Stevie Wonder (August 1963)
"The Ballad of the Green Berets" by SSgt. Barry Sadler (March 1966)
"Sunshine Superman" by Donovan (September 1966): Yes, he says "sunshine" and "superman" in the lyrics, but they're nowhere near each other in the song
"Ode to Billie Joe" by Bobbie Gentry (August 1967): Remind me to write sometime about what a great song this is
"The Letter" by the Box Tops (September 1967): A judgment call, since Chilton clearly sings "a letter" several times in the song, but I decided to include it since the title seems to refer to the overall theme rather than to serve as a quote from the lyric
"Indian Reservation" by the Raiders (July 1971)
"Theme From Shaft" by Isaac Hayes (November 1971)
"Brother Louie" by Stories (August 1973)
"The Joker" by the Steve Miller Band (January 1974): See "The Letter"
"TSOP (The Sound of Philadelphia)" by MFSB featuring the Three Degrees (April 1974)
"Annie's Song" by John Denver (July 1974)
"Theme From Mahogany (Do You Know Where You're Going To)" by Diana Ross (January 1976): Obviously, another judgment call. Do you know who directed Mahogany?
"Love Theme From A Star is Born (Evergreen)" by Barbra Streisand" (March 1977): See above
"Arthur's Theme (Best That You Can Do)" by Christopher Cross (October 1981): I'm glad "Nobody Does It Better" didn't stoop to this cheap trick
That brings us up to the Nineties, when I become unfamiliar with some of the Number One hits. I honestly don't know if Boyz II Men's "4 Seasons of Loneliness," from October 1997, included that phrase in the song's lyrics. I do know, however, that Berry Gordy directed Mahogany.