Triple Olympic Champion Jason Kenny failed to make it through qualifying in the event which left Crampton carrying the hopes of the British crowd.
And Crampton spoke of the significance of the Manchester event to him despite losing 2-0 to Australian Shane Perkins in the bronze medal race.
"The world cup in Manchester or any event in Manchester is bigger than the worlds and the bigger championships because it's always packed," said Crampton. "I'm from Manchester. I am Manchester. I love this track.
In the first bronze medal race Crampton took it on with over a lap remaining but failed to stop Perkins coming around the outside to take the win.
Crampton tried different tactics in the second race, opting to take a height approach, but it was to no avail.
Although he is hopeful he can go one better next year and make it onto the international podium.
"Hopefully things will start clicking into place," he said. "We're in a good training block so I think there is a bit more to come."
Meanwhile in the men's scratch race, Welshman Jon Mould claimed bronze as Britain's Owain Doull finished outside the medals.