The Croatian champions defeated Arsene Wenger's 2-1 in their Group F opener at the Maksimir Stadium on Wednesday night with a brilliant performance that had the 43-year-old coach beaming.
"Arsenal is one of the best teams who ever played here and they did exactly what we agreed they would do," said Mamic.
"We thought it would be very important to close the middle, to stop the fast passes."
An own-goal from Alex Oxlade-Chamberlain, forced by Josip Pivaric, and a sumptuous header from Junior Fernandes propelled Dinamo to a famous win on home soil much to the delight of Mamic who believes he tactically outshone Wenger.
"That's what we did and it's nothing new. We have already seen other teams who beat Arsenal use the same tactics. This is a good way to beat them," he added.
"Arsenal has top four top international players, and other top players compared to Dinamo, but they are not world class. We just concentrated in not letting them come to the ball. It was probably one our best games tactically."