The Aston Villa striker came on in the final stages in Dortmund and clinically slotted home the decisive goal in England's 2-1 win.
Watkins was teed up by another substitute, Chelsea's Cole Palmer, who also came on with him in the 81st minute.
"I said to Cole that we were both going to go on the pitch and he was going to set me up, at half-time," Watkins told reporters.
"It happened, I manifested it and as soon as he turned I knew I needed to make a move. You don't get that opportunity very often so I had to be greedy, I had to take it.
"After seeing it go into the bottom corner I don't think I've hit a ball that sweetly before. Obviously it's such a special moment."
Having been left out of all of England's matches at the tournament except for a 20-minute appearance against Denmark off the bench, Watkins said he had been getting itchy feet.
"To be honest, recently I got a little bit frustrated -- I don't like to be on the bench, I've had the best season of my career," he explained.
"The amount of people that have messaged me today saying I'm going to score tonight when I come on is ridiculous.
"Obviously they've put it out into the universe, hopefully they can do the same for the final or even give me the lottery numbers."
Watkins' dramatic goal was only the fourth of his international career and second in a competitive game, having netted the other against San Marino on his debut in March 2021.
The forward, in his first major tournament for England, described his joy at finding the net.
"When you score there's emotions that come through your body but this is just a different feeling," said Watkins.
"It was slow motion when I was running over to the boys and celebrating... I didn't want to get off the pitch at the end because I just wanted to soak it all in, it doesn't happen often obviously."
England face joint-record three-time Euros winners Spain in Sunday's final in Berlin, having finished as runners-up to Italy in the 2020 final.
"Spain are a great footballing team, so many good players, a lot of squad depth like ourselves, experience... it's the most important game of our lives," added Watkins.
