The goals came at the Estadio do Dragao in the round of 16 second leg, with William Gomes scoring in the 21st minute before Victor Froholdt added a second in the 72nd minute.
Hoeness had been quick to congratulate Francesco Farioli and his side, admitting Porto had been more clinical across the two legs.
"Congratulations to Francesco and his team on progressing," Hoeness said. "There were two matches, and one team were more efficient than the other."
Stuttgart had created opportunities on the night but failed to convert, something their manager believed had shaped the outcome.
"I wouldn't say the chances created fully justified this result," he said. "My team also put in a good performance. We created plenty of chances."
The Bundesliga side had pushed hard, particularly during a spell of sustained pressure, but they were undone despite their efforts, with Hoeness admitting one player had made the decisive difference.
"I think their goalkeeper had one of the best games of his career," he said, praising Diogo Costa. "He really helped the team get the result."
Hoeness had also pointed to positives, highlighting Stuttgart's persistence and attacking intent.
"Froholdt scored a brilliant goal with his weaker leg," he said. "We leave here with our heads held high. We played some very good matches."
He had again praised Porto's unity and quality, insisting their progression had been deserved.
"Porto were an amazing team, with real team spirit," Hoeness said. "There was one player who stood out, and that was the goalkeeper."