Dean Smith will oversee Leicester's final eight games of the season following the sacking of Brendan Rodgers last week.
Bournemouth did struggling Leicester little favours as a 1-0 victory plunged the managerless side even deeper into relegation trouble.
Leicester began life after Brendan Rodgers in similar fashion to how his reign ended as they slipped to a late 2-1 defeat to Aston Villa.
Leicester City have parted company with manager Brendan Rodgers as they look to maintain their Premier League status.
Roy Hodgson's second spell in charge of Crystal Palace began with victory as the hosts secured their first three-point haul of 2023 with a dramatic 2-1 win over Leicester at Selhurst Park.
Leicester drew at Brentford as Harvey Barnes snatched a point by scoring on Saturday afternoon to end their losing streak.