Mills was tipped to compete for a medal in the men’s 5000m after breaking Mo Farah’s British record in June.
A broken wrist from a fall later in the summer derailed his preparations and he looked way off the pace here.
At about the half-way stage, the Harrogate runner slipped back from the pack and then fell away badly, crossing the line last of the 16 runners.
Meanwhile, Sheffield sprinter Thompson was part of the men’s 4x400m relay team that finished sixth.
With Olympic silver medallist Matt Hudson-Smith and individual semi-finalist Sam Reardon both ruled out through injury, Charlie Dobson was the senior member of a quartet that also featured Toby Harries, and Davey, who tore his adductor in the mixed 4x400m relay on day one.
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He had recovered well enough to be named in the team for the final, replacing Seamus Derbyshire, the 400m hurdler who had helped them through the heats.
But the adductor limited Davey in the final on the third leg, with GB and NI having to settle for sixth, with Botswana taking gold in a dramatic finish ahead of the USA.
“We expect a lot more of ourselves, coming sixth in the final there,” Thompson said.
“We came here to fight for medals, and we know we’re capable of that, but it’s been a tough week in camp.
“We’ve navigated a few injuries within the team, but we’ve all come together as a squad and I’m proud of us. We’ve done really well under the circumstances.”
Meanwhile, British Athletics bosses vowed to leave no stone unturned after the worst return at a World Championships in 22 years.
Georgia Hunter Bell and Keely Hodgkinson claimed silver and bronze respectively in the women’s 800m on the final day, but GB and NI finish these Worlds in Tokyo without a gold medal for the first time since 2003 in Paris.
It comes off the back of Team GB earning the most athletics medals in 40 years in the French capital last summer.
Greg Rutherford was among those to criticise the relay performances, and performance director Paula Dunn admitted the rest of the world has caught up.
She said: “What we’re seeing now across the nations is that everybody’s investing in relays. Everybody, you know, the Dutch, the Germans. For me it’s like the marginal advantage we had has gone. We have now got to really focus in on it.
“Disappointment is sometimes a good thing. Because we have now got an opportunity to put things right.
“We want to be one of the best nations. But sometimes you have those years where it’s a rebuild year.”
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