Yellen's comments were more strident than they needed to be, were she only preparing markets for a December hike, they argued. Yellen suggested that the hike was conditioned on a premise that the data needed only to "continue to confirm" the Federal Reserve Open Market Committee's outlook.
The same message was delivered shortly after Yellen spoke by a second key Fed official, Vice Chairman Stanley Fischer.
The Goldman economists wrote: "Fischer was asked by Steve Liesman on CNBC later that day whether the 'strengthened' comment meant that we should be 'on the edge of our seats for a rate hike next month' (i.e. in September), he answered 'what the Chair said today was consistent with answering yes.' This wording sounded like a deliberate signal that both of them, not just Fischer personally, think September is on the table for a hike."
In his CNBC appearance on Friday, Hatzius said Fed officials made clear in the comments that they were looking for just confirmation of progress. He said: "151,000 is clearly about their estimate of what it takes to improve the labor market over time."
Wall Street economists had expected an unemployment rate of 4.8 percent, but it held at 4.9 percent. Wage growth slowed to a disappointing gain of just 0.1 percent while some economists had expected 0.3 percent.
Strategists had said a jobs report with nonfarm payrolls of 200,000 or more and strong components, like higher wages, would have possibly nudged the Fed to raise interest rates at its September meeting.
Goldman economists had forecast just 165,000 payrolls and pointed out the quirkiness of past August reports. They said August payrolls have fallen short of consensus by about 49,000 since 2011, but were revised higher by an average 71,000 in later releases.
The economists have also said this factor may make the Fed look past the initial September report.
They also said the economic data have been mixed but that GDP for the third quarter looks to be stronger, and their forecast is 2.9 percent.
"If they thought a hike made sense then (in June), it should make more sense now. In this context, it is also noteworthy that the number of regional Federal Reserve Bank boards asking for discount rate increases — a barometer of policy sentiment within the system — has risen further in recent months and now stands at 8 (the highest since December)," they wrote.
The Fed raised its fed funds rate for the first time in nine years last December but has held firm since then.