Great Britain Under-23 international King clocked 13.94 seconds in the 110m hurdles final at the Alexander Stadium.
British number one and favourite Lawrence Clarke won in 13.55, with Joseph Hylton second in 13.91 and Jake Porter third also in 13.91.
King’s attention will now turn to the European Under-23 Championships in Tallinn.
>He admitted he was frustrated to miss out on a medal in Birmingham.
The 21-year-old tweeted: “Disappointing day racing in Birmingham today, but I aim to bounce back in Tallinn next weekend for the European U23 Championships.”
Meanwhile, Erme Valley Harriers athlete Sam Trigg finished sixth in the triple jump with 15.37 metres.