Italy took the lead through top scorer Ciro Immobile just after the half-time break, but with barely ten minutes left to play, North Macedonia equalized at 1-1 when Enis Bardhi put the ball into the net.
With the loss of points, Italy is only third in Group C, although with two games less played than league leaders England. England drew 1-1 away to Ukraine on Saturday.
Spalletti, who last season led Napoli to the Serie A title, recently took over the Italian national team after Roberto Mancini moved to Saudi Arabia.