The club’s Head of Youth, who arrived from America in July last year, took charge for the side’s 4-1 win over Airdrie on Saturday after the sacking of Gareth Evans and departure of John Collins as director of football last week.
Goals from Iain Russell, Stefan Scougall and a Tony Andreu double saw off an Airdrie side who grabbed a late effort thanks to John Boyle.
The win moved the Lions up to third in the table and Burke says the new gaffer might struggle to fit all the deserving players into his match day line-up.
He said: “The boys have been absolutely fantastic over what was a very difficult 48-hour period, so to put a performance in like that was very pleasing.
“It’s going to be a tough job for whoever gets it. We’ve got some fantastic young players knocking on the door of the first team and it’ll be a tough job to fit them all in.
“The situation is up in the air and I really don’t know what will happen. At this moment in time I’m just enjoying the experience with the boys and looking to serve this football club – which is what I came from America to do – and see where it takes us.”
The visitors missed a glorious early opportunity after Jamie Bain was bundled over by Jesus Garcia Tena in the box after only three minutes, with Boyle blazing the spot-kick over the bar.
Livi soon went in front thanks to neat control and a smart finish from Andreu and the Frenchman added another with a low 25-yard drive after 38 minutes.
It was three before the break, Russell being sent clear thanks to a clever Scougall through ball and blasting past keeper Robbie Thomson.
The Lions finally added a fourth in 78 minutes when Scougall’s one-two with McNulty ended in the former slotting home, just minutes after Airdrie’s Sean Lynch was sent packing for two yellow cards.
Airdrie’s Boyle went one-on-one with Andy McNeil in stoppage time and tucked the ball into the bottom corner, but it was a meagre consolation for the relegation-threatened side.