See Ludwell Johnson “North Against South,” page 79 for the direct quotes. Lincoln did not write it in his diary. O.H. Browning scribbled what Lincoln told him, but Lincoln did write to G.V. Fox that provisioning Sumter was “justified by the result,” meaning war. Johnson does a nice job on the subject, pages 74-80 in North Against South.
See also Charles P. Roland, An American Iliad, pages 33-34.