The 27-year-old, who only returned to action last month after nearly five months out with a broken leg, rose at the near post to head Shaun Maloney's corner past Joe Hart.
He told Sky Sports: "It's an incredible achievement. Today, all the lads were fantastic. It was a great performance and thoroughly deserved.
"I just wanted to get on the pitch. Once I got on there, they went down to 10 men and we knew that this was our chance, our chance to win an FA Cup.
"We stuck to the game plan and we created chances.
Watson hopes Wigan can now secure their Premier League status be replicating their Wembley heroics in their final two games against Arsenal and Aston Villa.
He said: "It's a huge boost. We have got two massive games coming up and if we perform like we did today, we're capable of picking up the points. But we are going to enjoy today and then get back into training tomorrow."
Maloney and James McCarthy were both quick to praise manager Roberto Martinez after the match.
McCarthy said: "I think the gaffer is a tactical genius. It's down to his tactics what we've done.
"It's an unbelievable achievement. I'm speechless to be honest. It's a dream come true, it's what you dream of as a kid."
Maloney added: "Considering the size of the club it's incredible. For Ben to score the winner after the season he's had, it's amazing for him.
"Tactically Roberto is as a good manager as we could have asked for."