As Bryan's team mates celebrated around him, the fullback revealed the content of a sideline conversation he had with his boss just before opening the scoring in the 105th minute with a free kick from deep that flew past Brentford keeper David Raya.
"(Parker said) whip it in the near post, because the keeper comes ridiculously far off his line. That's something we practised this week," Bryan told Sky Sports.
Parker confirmed his instructions to Bryan, who added a second goal in the 117th minute to kill the game off.
"We looked at Raya's positioning from free kicks, he's very, very aggressive, he's very aggressive in his starting position," Parker explained.
"I told him (Bryan), 'You need to keep an eye on his positioning, and I want you to commit to it, I want you to commit to the shot', and it's worked," he added.
The 26-year-old defender's second goal came after a lung-bursting sprint to play a one-two with substitute Aleksandar Mitrovic before slotting the ball home and this time he credited his fitness regime during the novel coronavirus lockdown.
"I'm quite fit, you know! In lockdown all we could do was run. That's all I've been doing, running, and it's paid off today," he said beaming.
Former Fulham captain Parker, 39, was delighted with his side's performance and gave credit to his players and backroom staff for bouncing back to the Premier League following their relegation last season.
"I'm the one that fronts it up, I'm the one that everyone sees but behind the scenes is a support network that keeps you going ... I'm very proud of my team," he said. (Reporting by Philip O'Connor; Editing by Ken Ferris)