The central midfielder - who nabbed the unlikely late winner against Manchester City in last year's final - fired a superb first-half strike from around 30 yards.
But, speaking after the 2-1 win at Cardiff City Stadium, Rosler revealed he was looking the other way at the time.
"I didn't saw (see) the second goal," he said. "I just turned around and the ball was in."
Despite a commanding performance, Watson was taken off early in the second half.
Rosler revealed the decision was a combination of precaution over an existing injury, and wanting to see how replacement Josh McEachran, a former Chelsea trainee, would handle a pressure situation.
Rosler added: "We take it game by game. I felt very happy with the performance, the application.
"Our supporters travelled in big numbers. We made them proud, we wanted to make them proud.
"I wanted to compete against the best teams in the country and Cardiff today gave us the possibility, and we stood our own ground very well.
"We've beaten now two teams (Premier League) on the way and we're now in the last eight."
Rosler's focus now switches to Barnsley in the Sky Bet Championship on Tuesday night, as the Latics continue their push for the play-offs.
Meanwhile, Bluebirds boss Ole Gunnar Solskjaer has to prepare for a Premier League relegation battle.
Showing support for his opposite number, Rosler said: "We are friends and Ole Gunnar is a winner. I said that before the game.
"He knew exactly what he got himself into coming to Cardiff and he can make it happen. He knows exactly what he's doing and you see already what he tried to achieve in terms of styles of play.
"He wants to attack and he will be fine. I have no worries about that."
Midfielder Chris McCann opened the scoring, before Bluebirds striker Fraizer Campbell equalised with a low drive.
Despite some nervy moments in the last 10 minutes, as Cardiff pushed and pressed for the equaliser, Wigan held out to keep their dream of a second successive FA Cup trophy alive.
Reflecting on the loss, Solskjaer said: "I wouldn't even say pretty disappointing. It's very disappointing, because we had the majority of the possession, the majority of the shots, more chances, but when you don't take chances you're not going to win games.
"The first goal to concede is a poor one. I thought it was a stupid foul to give away, then we don't clear our lines.
"We should have headed it clear, but the second goal we can't do anything about - that's a wonder strike by the kid. That was the two shots they had on target."
Despite losing to a team from the Championship, which Cardiff won and got promoted from last year, the Norwegian added: "They are a good side. They are the holders, he's (Rosler) done really well with them for the months he's been there.
"They play good football, they've got good players - probably got more Premier League experience than we have - so of course we didn't play mugs, we played a good team with good players."
Looking to how his side will tackle the challenge ahead, Solskjaer added: "I don't know any other way than work hard, believe in what you're doing, don't feel sorry for yourself.
"That's the only way to get out of a bad spell as a footballer, as a team, as a club and that's what you've got to do.
"You've got to believe in each other, trust in each other and we've got a big, big game next weekend - Hull."
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