The 20-year-old striker agreed to join Belgian outfit Standard Liege on a five-year contract with Celtic receiving a fee of £1.2m.
Miller was an interested onlooker as Watt was catapulted into the spotlight following his winning goal against Barcelona in the Champions League group stages in 2012.
The youngster failed to take the next step, however, and spent the duration of the last campaign in Belgium with Lierse.
Miller, who won a Premier title and two Scottish Cups at Celtic, said: "Having watched how it has gone for Tony since that night against Barcelona, I felt he had to leave because it just wasn't going to happen for him at Celtic. He was always a fringe player.
"Even when they played Barcelona that night, he was on the bench. Tony will forever be remembered for that. But, in reality, he didn't do much else."