The Spaniard's 93rd-minute winner completed a dramatic turnaround at the Emirates Stadium, after Bukayo Saka's first half opener had been cancelled out by a Riyad Mahrez penalty before the hour.
And the Spaniard was delighted by the manner in which City kept pushing right until the end.
He said: “We struggled in the first-half but took control in the second a bit more and do more our game.
“They did a great game but we showed our champions personality.
“We’ve learned from the last years you have to push always no matter what happens.
“We didn’t do a great game but we pushed, we never dropped and we always thought it was possible.
An incident packed second half was brought to life when Bernardo Silva was brought down by Granit Xhaka inside the box just before the hour.
Referee Stuart Atwell initially waved away the Portuguese midfielder's protests but, after a VAR review, revised his decision.
Xhaka and a number of his Arsenal teammates were incensed by the decision after a first half penalty shout of their own wasn't investigated by VAR, with Martin Odegaard going down under the attentions of Ederson.
And their frustrations compounded soon after when Gabriel was shown a second yellow card for a late challenge on Gabriel Jesus.
Nonetheless, Rodrigo was under no illusions that referee Stuart Atwell called the shots correctly in London.
"I have no doubt ours was a penalty”, he explained.
“At first I had doubt in the first action, but I got close to the screen (on the VAR review) and for me it is clear.
"Small details make a big difference. They made a big mistake with the second yellow for Gabriel.
“We were clever, we did not have many chances but we were so effective.”