But he was cruelly denied as, having already suffered a puncture to his front wheel, a rear puncture proved a technical fault too far.
"I was trying to keep my pace up but it was like doing another 20 miles on top," he said.
"When Josh caught me I knew it was impossible. Usually people stop, but even with the front tyre I thought I had enough to win.
Marathon punctures frustrate Weir
"It is a nightmare because I was in the best shape coming into this one. It was the fastest I had pushed London, but I felt great even when I was on my own."
Cassidy, who was sixth in last year's New York race, celebrated a breakthrough into the world's elite after coming home in came in one hour 35 minutes and 21 seconds.
"It means so much. I have been finishing around the top five quite often, but to establish myself as one of the top guys really means a lot to me," he said.
Cassidy 'been waiting long time' for win
In the women's race Tsuchida and Graf both edged out defending champion Amanda McGrory in a sprint finish with Tsuchida making it back-to-back marathon wins after triumphing in last week's Boston Marathon.
Britain's Shelly Woods, who had led earlier in the race, dropped out of contention before the final stages and eventually finished fifth after suffering a puncture of her own.
"I was with the girls at 21 miles, was feeling really good and the tyre just went pop and that was the end of my race. There is nothing you can do about it," she said.
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