The 21-year-old, running for Great Britain, had qualified fastest for the 110m hurdles final by winning his heat in 13.74 seconds the day before.
But in the final, King, running in lane six, could not produce a clean run over the barriers and paid the price by missing out on bronze by just four hundredths of a second.
His GB team-mate and World Junior medallist David Omoregie won the event in 13.63 seconds.
Spain’s Javier Colomo came second in a personal best time of 13.73, with Italia’s Lorenzo Perini third in season’s best 13.86 and King fourth in 13.90.
Afterwards King tweeted: “Never thought I’d be so disappointed with 4th at the European U23 Championships! Thanks to everyone that helped/supported.”