The British runner fell just short of the 800m world title in a thrilling race with Mu.
She finished eight hundredths of a second off Mu.
The pair went toe-to-toe down the final 100m, but couldn't pass her for victory.
Hodgkinson said he gave everything up to the line.
There is a world silver. Fuel is added to the fire. I have more titles to come so I will have to focus on that.
I am looking forward to next year because I want to get more.
Hodgkinson's rivalry with Mu, also 20, seems set to define the event for the World Championships in Budapest in 2023, the Olympics in Paris in 2024 and, possibly, many years later.
The tension of their contest was evident as they were introduced to the crowd.
The race boiled down to the face-off down the back straight after they hit the bell.
The first move was made by Mu, who stretched her legs to open a lead.
The British woman dragged herself back along with Mu and appeared to be about to steal.
Mu held on to gold and held her opponent at bay.
As she collected her breath after the finish line, Hodgkinson motioned to her team in the stands, her finger and thumb set a couple of inches apart.
There is a small gap between the two. She will be reminded by coach Trevor Painter and JennyMeadows.
In the 49th and final medal event of the Championships, Great Britain's 4x400m quartet of Victoria Ohuruogu, Nicole Yeargin and Laviai Nielsen won a bronze.
The United States won a gold medal and Jamaica took the silver.
For the first time in four years, Great Britain have five different individual medal winners.
Great Britain finished with seven medals, with the 4x 100m relay team taking bronze. It's the same amount as the haul taken on home soil at London 2017, and by a team including Mo and Jessica.
Steve Cram, a former world champion and commentator for the British team, said it had gone better than expected.
Concerns were raised about Dina's form and whether she could convert again. Laura was also hurt. We were expecting three to five medals in the spring.
The British took their chances and it has been a great championship. Heading into an important cycle with the Paris Olympics, that is good news.
The US won a record 33 medals, including 13 golds. They had clean sweeps in the men's 100m, men's 200m and men's shot put.
In the 5000m, after being beaten in the 1500m earlier in the week, he bounced back with a win.
After his loss to Wightman, the Norwegian thought he would end his season, but changed his mind and won the world title.
Joshua Cheptegei, who won the 5000m gold medal at the Tokyo Olympics, finished in ninth.
The gold medal went to Nigeria's Tobi Amusan, who ran a world record in the 100m semifinals earlier in the day.
Amusan's winning time of 12.06 seconds would have been an improvement on the 12.12 second world record she had set a couple of hours before but was ruled ineligible by a tailwind.
The national record that Cindy Sember set in the semi-finals would have been lowered if she had come fifth.
Two Britons finished in the top 10 in the long jump. Germany's Malaika Mihambo jumped out to 7.12m to defend her world title.
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