The duo both featured for the Baggies in the League Cup clash with Brentford back in September.
But with Ivanovic arriving as a free agent and Gallagher hardly featuring for parent club Chelsea during pre-season, Bilic wanted to give them the international break to work on their fitness before playing them in the Premier League.
And Bilic thinks the duo showed exactly why he was so keen to bring them to The Hawthorns.
“Ivanovic showed exactly why we wanted to sign him,” the head coach said.
“Experience, shape, leadership, quality, calmness.
“We were able to build up when we had possession because the two centre-backs were really calm on the ball.
“Both of them (Ivanovic and Ahmed Hegazi) coped extremely well with Burnley’s two strikers – their strikers are their game, basically, they’re high quality strikers – so the good crosses are coming.
“They limited them to extremely little. I’m really pleased with the way they played.
“Conor – even if this was his 50th game, I’d have said he did well.
“But considering this was his Premier League debut, he impressed me.
“Very brave, good skill, great legs, extremely front footed and reliable and responsible. He impressed me a lot, he should be very proud with his debut.”