Funerals are especially difficult to do when it appears the deceased did not know Christ. (Today’s funeral was for one who professed faith in Christ.) The sorrow of the unbeliever is different from the sorrow of believers. Both are sorrowful, but unbelievers are often deep in despair and it is difficult to extend any significant comfort them since the promises of God are for those in covenant with him.
What does one do in this situation? The same thing you do in any situation: preach Christ. (You must do this without preaching the deceased into heaven or hell.) It is difficult, but it is the preacher’s calling to preach Christ and to hold out faith in Christ as essential to receiving and resting in the promises of God.