The 21-year-old defender made his debut for the Bhoys against the Dutch giants at the Amsterdam ArenA in Amsterdam in the Europa League.
The Croatia Under-21 international centre-back, who joined Celtic from Dinamo Zagreb in the summer transfer window, started the Group A encounter and played for the entire 90 minutes.
Celtic boss Deila was pleased with the performance of Simunovic and spoke highly of him after the match, which ended in a 2-2 draw.
RD on Jozo Simunovic's debut: "He did very well. You can see he's going to be a good player for us." #UEL (MH)— Celtic Football Club (@celticfc) September 17, 2015
Ronny Deila's Celtic took the lead in Amsterdam as early as the eighth minute through Nir Bitton, but Viktor Fischer restored parity for the hosts with a well-struck shot on 24 minutes.
Mikael Lustig headed home for the Hoops three minutes before the half-time interval, but Lasse Schone made it 2-2 with a free kick in the 84th minute after Emilio Izaguirre was sent off for a second bookable offence.