The 22-year-old finished fifth in the breaststroke sprint, 0.37s behind winner Mark Warnecke. The German powered out of the blocks and despite the likes of Cook battling back at him in the second half of the race Warnecke hung on for gold.
Cook set his third personal best of the championships when winning his semi-final from lane one in 27.91s. However, the City of Newcastle swimmer, who was Britain's sole representative following James Gibson's shock semi-final elimination, failed to repeat his form in the final and fell away in the final 20m.
America's Mark Gangloff claimed the silver in 27.71s, with Japan's Kosuke Kitajima took the bronze.
Cook said: "I think I deserved a medal. I worked really hard but it just was not good enough. I was flowing for the first 30m and then it started to slip away.
"I didn't have a good finish like I did in the semi-final. I was in the final just to get some experience and have some fun. I have learned a lot about myself and that's important. The guys in the world have now been introduced to what I can do and hopefully there is still more to come."
Britain's Melanie Marshall produced a disappointing showing in the final of the 200m freestyle, trailing home in seventh spot.
The 23-year-old from Boston finished 0.76s behind France's Solenne Figues, who claimed the gold in 1:58.60s. Italy's Federica Pellegrini took the silver in 1:58.73s, while China's Yu Yang took the bronze.
"I am so annoyed at that performance I messed up again and that is frustrating," said Marshall. "This is my first senior individual final, it's a big step in the right direction but the result was still garbage."
American Michael Phelps is on course for his third gold medal in Montreal after qualifying for the 100m freestyle final.
Phelps, who claimed gold ahead of Australian Grant Hackett in Tuesday's 200m freestyle, qualified fifth fastest in a time of 48.93s, 0.48s behind the quickest man in the semi-final, South Africa's Roland Schoeman.
Former world record holder Michael Klim could only manage the 11th fastest time and surprisingly crashed out.
On Tuesday evening, Britain's Rebecca Cooke had trailed home a disappointing seventh in the 1500m freestyle final.
The Glaswegian swimmer took the fastest qualifying time into the final but despite holding third position in the early stages of swimming's 30-length endurance race, soon faded from the podium places.
The American teenager Kate Ziegler claimed gold, finishing just outside the 16-minute barrier in a time of 16:00.41s. Swiss swimmer Flavia Rigamonti took silver with home-crowd favourite Brittany Reimer finishing with the bronze.
Cooke was well adrift of the top three her time of 16:23.25s was nearly 10 seconds slower than her two-year-old British record and nine seconds adrift of the mark she set in the heats on Monday. Cooke said: "I have to assess how I swim in the heats and conserve my energy better for finals.
"I rarely swim back-to-back 1500m at international level. I have not swum this distance in over a year, so two races in two days is quite a lot for me."
There was also disappointment for the defending men's 50m breaststroke champion, James Gibson, who failed to advance beyond the semi-finals. He finished 12th fastest in the semi-finals in 28.18s eight-tenths slower than his personal best two years ago.
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