Suarez's brace at the Etihad Stadium put Barca in command of the last 16 tie before Sergio Aguero pulled one back for City.
Lionel Messi spurned a chance for a late third away goal as his penalty was saved by Joe Hart, with the Argentina star surprisingly heading wide on the rebound to keep City in with a chance of turning things around at Camp Nou.
Suarez has long played the role of the pantomime villain in England for his various indiscretions while at Liverpool.
He was given a typically hostile welcome by the City fans but, according to Suarez, that only fuelled him to provide a clinical demonstration of his goalscoring prowess.
Suarez told UEFA.com: "Obviously it is pleasing, first of all to be able to help the team with important goals in a Champions League knockout game [and] of course to come back to England and [win] against a team you're always motivated to play against.
"There are certain types of players like me who get more inspired, more motivated when fans boo them - it helps motivate you a bit more."
Much was made of City boss Manuel Pellegrini's decision to deploy a 4-4-2 formation against one of Europe's top sides, and Suarez indicated that the extra space afforded by the hosts' set-up was key to Barca's success.
"We produced a really good game, the team in general, and managed to take advantage of the space City left open," he added.
"We were clever in our reading of the game and we created a lot of openings and could have scored another goal."
