Adcock, who partnered Imogen Bankier in the mixed doubles badminton competition at the London 2012 Olympics, and Ellis produced the best British performance by reaching the semi-finals in Basel.
However they couldn't go one better and make the men's doubles final as they lost 21-19, 21-19 to Ko and Lee, ranked third in the world, in 47 minutes.
Adcock and Ellis trailed 17-13 in the opening game before pulling level at 18-18 however they couldn't push on and take the first set in Basel.
They led 12-10 and 13-12 in the second game and fought to 19-19 after letting the Korean pair back in but lost the next two points to fall 21-19.
Elsewhere in the men's doubles draw in Basel, Scot Robert Blair and Malaysian partner Bin Shen Tan came through qualifying but didn't advance past the first round.
Fellow Brits Chris Langridge and Peter Mills and Marcus Ellis and Paul van Rietvelde also fell at the same stage as did Lauren Smith and Gabby White in the women's doubles.
Heather Olver and Kate Robertshaw fared better as they progressed to round two before losing while the former combined with Langridge to reach the quarter-finals in the mixed doubles.
Adcock and White lost in the first round while Rajiv Ouseph reached round two of the men's singles.