Semenyo netted a brace at Anfield, to haul the Cherries back level with their hosts at 2-2 with 14 minutes to play, although they went on to lose 4-2 after two late Liverpool goals.
The Ghanaian also reported racist abuse from a fan during the first half when at 0-0, with the game momentarily paused by referee Anthony Taylor.
Bournemouth trailed 2-0 after 50 minutes, but Semenyo turned the game on its head with two goals in 12 minutes to bring the visitors level - after he scored a brace in the final game of last season too, against Leicester.
Both came after rapid counterattacks.
The first saw Tyler Adams play a brilliant ball in behind the Liverpool defence for David Brooks to race onto, and the Welshman produced a pinpoint cross into the centre of the box for Semenyo to sweep past Alisson.
But the pick of the two goals was his second.
Match report:
Liverpool gave the ball away on the edge of the Cherries box and Hamed Traore set the ball to Semenyo midway through the Bournemouth half.
He drove forward with a four-on-two, but opted to go it alone, firing a low shot into the bottom corner from just outside the box.
His performance was particularly impressive in the context of what had happened in the first half, with Iraola saying he was calm and composed during the game.
Asked about the Ghanaian’s showing, Iraola told the Daily Echo: “Antoine has started the season the same way he finished first one.
“He was creating I think a lot of problems to the full backs and [they are] different goals. First one more like a combination through the left because we were, I think, putting a lot of crosses from the left and he arrives well.
“Second one is also a transition but more he takes it by himself and it's a good finish.
“It's a shame that coming here scoring two goals at the end you go back home with nothing, but obviously we can find positives.”