Sterling went down under the faintest of contact and after a VAR check, the referee’s decision to award a spot kick was deemed correct.
Kasper Schmeichel saved Harry Kane’s penalty but Kane slammed home the rebound to send England into the final on Sunday, where they will face Italy.
It was cruel on Denmark, who had battled bravely as they have done all tournament, but England deserved the win and were the better team for long periods.
Unsurprisingly Sterling defended the penalty decision in his favour, adding: “I went into the box and he stuck his right leg out, and it touched my leg so it was a clear penalty.”
Despite the celebrations at Wembley, Sterling insisted the focus would almost immediately shift to the final against Italy.
“It’s another step in the right direction,” he added. “But once we’re back in the dressing room it’s over and we’ve got to focus on the weekend now. It’s step-by-step and that’s all we can do.
“It was a top performance – we had to dig in deep after the first goal we conceded in the tournament, and we regrouped well and showed a good team spirit to come back and win the game.
“It was difficult going behind but we knew we had to stay patient – we knew with the legs we’ve got, the aggressiveness and the power we have in the team, it would be a matter of time before we broke them down.”
ITV pundit Ian Wright admitted there was an element of luck in the winning goal, but said Sterling has been the stand-out performer for Gareth Southgate’s side.
“There was a bit of luck with the way it came about, but all the years waiting, maybe that’s the luck,” he said. “I’ve been dreaming of this day and now it’s come, I can’t believe it’s here.
“Raheem Sterling has attacked this tournament. I believe he was the difference, I am delighted for him, Gareth and the whole country. I am speechless because I want England to win something in my lifetime.”