Suhr, who set a world indoor record in March and along with Yelena Isinbayeva is one of only two women to have ever cleared five metres, put her defeat down to tiredness from a late arrival in London and trying out new poles in competition for the first time.
London silver medallist Silva, beaten on countback in the Olympic final, won with a clearance of 4.83m. Suhr could only muster 4.73, good enough for second but down on her outdoor season's best of 4.80.
"What's amazing is I was on bigger poles than I've ever been on," Suhr told Reuters.
"Really it was just about trying to get the timing right at this meet. The exciting news is that I've now been on poles I've never been on before."
Silva, with the five leading leaps in the world this year, is clearly the woman to beat at the world championships in Moscow next month, where twice Olympic champion and world outdoor record holder Isinbayeva is set to bow out from a sport she took to new heights.
"It's going to be some final," Suhr said.
"But I just have to focus on myself and my jumps right now. I'm really excited looking forward.
"Training has really been going well, it's just sometimes I think you are jumping better than your story and that's it right now.
"I'm jumping a lot better than what I'm putting up."
- Sports & Recreation
- Yelena Isinbayeva