The American replaced Marcelo Bielsa, who was sacked on Sunday, earlier this week and will have been pleased with elements of his side's performance, with a noticeable improvement defensively.
But ultimately Barnes' goal proved decisive to inflict a fifth straight defeat, and sixth in seven games, that now leaves Leeds in a precarious position in the Premier League table with their relegation rivals still to play this weekend.
For Leicester, successive wins and clean sheets means they move back in to the top half.