The EP only freed the slaves within the states that were in rebellion, straight from the EP itself: all persons held as slaves within any State or designated part of a State the people whereof shall then be in rebellion against the United States shall be then, thenceforward, and forever free
Slaves in states that did not secede, Maryland, Kentucky, Delaware, Missouri, were not freed until passage of the 13th Amendment after Lincoln's death.
President Lincoln insisted that the 13th amendment be made a plank in the 1864 Republican Party platform. This despite the fact that it appeared for a time that he was sure to lose.
He worked hard for the 13th amendment, and it passed because he did a lot of arm twisting to get it done.
Don't forget that in that same time frame, he was urged to rescind the EP altogeher. He refused.
David Donald writes:
"As he talked to them, his impatience with the War Democrats became increasingly evident. If they really wanted the war to end without interfering with slavery, 'the field was open to them to have enlisted and put down this rebellion by force of arms long before the present policy was inaugurated'...."
"How could anybody propose 'to return to slavery the black warriors of Port Hudson and Olustee to their masters to conciliate the South? I should be damned in time and in eternity for so doing,' he told his visitors. 'The world shall know that I will keep my faith to friends and enemies, come what will'."
Not entirely true. Slaves in Missouri and Maryland were freed when those states amended their Constitutions prior to January 1865. Slavery was ended in the District of Columbia during the war, 1862 if memory serves.