Four athletes cleared at 4.55, including German Liza Ryzih, Sweden's Angelica Bengtsson and Canadian Alysha Newman, plus Silva.
Ryzih and Silva then cleared 4.65m to set the pace in the event.
Silva went on to win the event, with a best of 4.81m after having three misses at 4.92m. Russian Anzhelika Sidorova, competing under a neutral flag, took second with 4.75m and German Liza Ryzih was third.
"The wind was pretty tricky out there. Everyone was struggling a little bit," McCartney's coach Jeremy McColl said from Oslo.
"It was one of those days. In pole vault anything can happen."
McColl said McCartney, using her shorter 10-pace runup, had warmed up well, they had done a few training sessions since the Rome event and all is in good shape, despite today's disappointing mark, which he puts down to a demanding wind and "the luck of the draw really".
"It was really swirling, not coming from any (one) direction whatsoever, so it was throwing all the marks around a little.
"It was very hard to judge what the wind was doing but that's what it does in stadiums like this.
"You can be halfway down the runway and all of a sudden it changes and your marks are wrong."
This is McCartney and McColl's first visit to both Oslo and Stockholm, where they head to tomorrow for the next Diamond League meeting on Monday morning (NZT). He chalks it up to a valuable learning experience for McCartney.
"Everything's going well, she's pretty good.
"It's how she bounces back from this. She'll take a bit out of it.
"She's happy, she's fine but it's just trying to learn from it and (so) we can build on it coming to the major championships."
McCartney's prime target this year is the world championships in London in early August. She has competed in London before so there shouldn't be any surprises.
