In a strong field, Muir clocked 4:11.48 to finish behind world record holder Genzebe Dibaba, Commonwealth champion Faith Kipyegon, European champion Sifan Hassan and Ethiopia's Dawit Seyaum.
"I'm really pleased. That was such a tough field," said the Scot, 22.
"I think any other year I probably would have medalled."
Muir added: "I expected it to be hard - it's a championship final.
"There are so many girls in there, you don't know who is going to do what but I was prepared for a fast race or a slow race and I just worked on staying out of trouble.
"This is the first time I've done three rounds, so to have got three and done them well, my preparation for [the Rio Olympics] next year is good."
Muir - who was three seconds behind Ethiopian winner Dibaba - said she was pleased to have posted a good time in Beijing after missing out on the 800m final at last year's World Indoor Championships and not picking up a medal at the Glasgow 2014 Commonwealth Games.
"I left last year so frustrated as I knew I could run so much better but it's great to have come here and have done well in the final," she added.

Previously, councillors deferred a decision to grant permission to build a supermarket that would have paid for the stadium, which supporters claimed had put the plans in jeopardy.
A partnership is now revising the proposals to see if the stadium can be built using money from smaller shops.
The plans are expected to be discussed by Cornwall Council members in May.
Truro and Penwith College, the Cornish Pirates rugby club, Inox Group and Henry Boot Developments are behind the revised plans for the multi-use stadium at West Langarth.
Julian Painter, director at Henry Boot Developments, said: "A supermarket would have provided funds sooner and generated more value.
"That is no longer an option but we are not giving up."
The supermarket plans were deferred earlier in March, but two other major retail developments in Truro were approved, which supporters claimed effectively marked the end of that proposal.
Mr Painter said the new proposal would split the original supermarket unit into smaller stores - including one retail store and non-food units.
He said the partnership was trying to "squeeze enough value from the development" to deliver about £8m of funding, with a further £2m coming from Truro and Penwith College, which will provide the £10m needed for the 6,000-capacity stadium.

20 December 2015 Last updated at 13:02 GMT
Andrew Russell, 36, was found unconscious in a car park on Bradshaw Way, in Derby, shortly before 02:00 on 16 November. He was taken to hospital but later died.
Det Insp Graham Prince, of Derbyshire Police, said: "We are trying to trace a number of cars seen driving along London Road between 1.30am and 2.15am that morning, along with several lone people walking down the road during the same time period.
"These people have yet to come forward and they could have information which may help with the inquiry."
A 41-year-old man has been charged in connection with the alleged attack.
Britain's Laura Muir said she was delighted with her fifth place in the 1500m final at the World Athletics Championships in Beijing.
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Revised proposals for a stadium in Cornwall are expected to be submitted to the council.
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Detectives investigating a fatal assault have released CCTV footage of potential witnesses who have yet to come forward.