Philip Seymour Hoffman's GF & Children -- Emotional Funeral Exit

Sad day in New York City Friday -- Philip Seymour Hoffman's longtime girlfriend Mimi O'Donnell and their 3 children just exited the Manhattan church where the actor's funeral just ended ... and it was emotional.

Mimi -- flanked by 10-year-old son Cooper, 7-year-old daughter Tallulah and 5-year-old daughter Willa -- exited the Church of St. Ignatius Loyola together moments ago.

Other famous attendees also found it difficult to contain their feelings -- Jake Gyllenhaal and Michelle Williams left together, both wearing dark sunglasses. Michelle held her hand over her mouth.

It's tragic ... Gyllenhaal was set to star in Hoffman's upcoming directorial effort "Ezekiel Moss" -- in fact, his involvement in the film was announced just days before Hoffman's death.

Williams starred with Hoffman in "Synecdoche, New York" in 2008 -- the same year her ex Heath Ledger also OD'd on drugs.