The 26-year-old winger rediscovered his scoring touch as City defeated AC Omonia 2-1 on the night and 4-2 on aggregate.
Wright-Phillips got the crucial second against the Cypriots in the 55th minute after skipping past two defenders.
It was his fourth goal in his second spell at City after his £9million return from Chelsea in August and came on the back of Elano's opener seven minutes earlier.
Hughes said: "Shaun was a little bit frustrated at playing the wrong ball at the wrong time.
"But he kept going. He gives us great energy and great pace down the right-hand side. His goal was just reward for his efforts."
Elano's goal was also one to savour after City has struggled to build on their 2-1 advantage from the first leg of this first-round tie.
Latching on to a crossfield pass from fellow Brazil team-mate Robinho, he lashed a shot into the corner to ease the home fans' nerves.
Hughes is pleased at the way the partnership is developing.
"Elano is coming into a bit of form," said the City boss. "He is playing on the left alongside Robinho and they are working well together.
"They already have a good understanding of each other and that can only benefit us in the games to come."