The 20-year-old earned a 12-minute cameo in the win over Watford.
Joe Allen gave Liverpool a slender 1-0 half-time lead following an opening 45 minutes in which the Hornets had looked dangerous, but Roberto Firmino came off the bench to make sure of the victory on 76 minutes.
Klopp again fielded a number of young players in his first XI, with one eye on the upcoming visit of Chelsea in the Premier League, and young Brannagan, who turned 20 today, replaced fellow academy prospect Sheyi Ojo with 12 minutes to go.
The midfielder enjoyed a promising cameo on the right-hand side of midfield, perhaps in a vaguely unfamiliar role, and Klopp admits he did not expect the starlet to impress him as much as he did.
"Cameron Brannagan I told him when he came on 'It's not your position, sorry' but after the game I had to say 'okay, forget it, you can play this position too'. He was really good," he said via the Liverpool Echo.
Brannagan could, and perhaps should, have registered an assist after standing a brilliant cross up for the unmarked Christian Benteke late on, but the Belgian striker headed over the crossbar as the chance went begging.