Conrad Murray -- I Was Only Trying to 'Tip' Michael Jackson Into Sleep

Conrad Murray claims he was only trying to "tip" Michael Jackson into sleep when he gave him a "tiny bit" of Propofol the morning MJ died -- and it's the first hint at what the doctor might have said on the stand.

Murray went into stark detail about June 25, 2009 during the documentary "Michael Jackson and the Doctor: A Fatal Relationship" ... which aired on MSNBC.

In the documentary, Murray says he eventually gave in to Michael begging for "some milk" ... Propofol. Murray says he thought ... "If I give him just a tiny amount of Propofol ... 25 milligrams, slowly infused, I may just tip him into sleep ... and the other medications will now get a chance to work because he had a fair amount of medication on board."

According to Murray's recorded interview with police -- two days after MJ's death -- he had already pumped MJ with sedatives -- Valium, Lorazepam, Midazolam -- but the singer was still unable to fall asleep.

in the docu, Murray claims it was the other drugs -- not the Propofol -- that "overwhelmed" Michael. Of course, Murray also gave MJ those other drugs ... at least according to what he told police.