The third-year veteran exuded confidence running the offense and showed strong decision-making under pressure.
Joseph on Monday called Siemian the "clear-cut" winner, despite whispers last week that Lynch had showed well during a recent string of camp practices.
"It was close, in my opinion, probably in mid-camp when Paxton was making huge strides fast," Joseph said. "But I said the games were going to be an important piece, and games were. And in my opinion, Trevor played better than Paxton in actual games."
For his part, Lynch was "very disappointed" with not winning the starting QB job.
"I gave everything I had to go out there and win the job," Lynch told reporters Monday. "But the coaches made their decision, and now I'm at the point at where I'm at. I just got to prepare and be ready because a lot of guys in this league are always one play from getting in, so that's how I'm going to prepare."
While the Broncos have a competent starter in Siemian, the organization still must find a way to develop a first-rounder in Lynch looked far from ready in live game action.
"Well, that's on the coaches, and that's during practice, as far as how we coach him, that won't change, and as far as his reps in practice, that won't change," Joseph said. "The more he plays, the better he will be as a quarterback."
Broncos football czar John Elway hand-picked Lynch to take over under center, but that transition is on hold. Joseph, though, emphasized that Lynch remains a key player in Denver's future plans.
"We're playing Green Bay this week and Aaron Rodgers didn't play for a long time. Now, he was behind [Brett] Favre, a real guy like that. But still, I don't believe that [Lynch is a disappointment]," Joseph said. "He's a guy with real talent. With time he will be a good quarterback, but right now, I think Trevor's the best guy for our team."