As an economist not a historian, No. Historians may be interested in adding more historical detail, but I can give a brief history with reference to the relevant economic theories.
There were two periods of economic crisis in the 1970s and early 1980s, both characterized by high inflation, high unemployment, and low growth. The first was the recession of 1973-1975. The second was a period of rising inflation starting roughly in 1978 and culminating in the recessions of 1980 and 1981-1982 (although high inflation had ended by late 1980 or early 1981). Both of these periods of crisis were somewhat global. The biggest causes were the 1973 oil crisis (Saudi Arabia and OPEC embargoing nations that supported Israel in the Yom Kippur War) and the 1978 food price shock and 1979 oil crisis (following the Iranian Revolution and continuing into the 1980s with the Iran-Iraq War). There were other important causes as well, that I'll mention below.
There are two main explanations for stagflation, which may be called supply shock and demand shock respectively. Supply shock is usually given primacy, even by those who write about demand shock hypotheses.
Supply shock
Many cases of inflation are caused by excess money supply, but under this hypothesis inflation has a different cause, increased prices of commodities. The oil crises led to an increase in energy prices, which led to a type of inflation caused by a contraction of aggregate supply (the global economy was willing to supply a smaller quantity of goods and services). In this situation, input prices increase without a correlated increase in productivity. When aggregate supply shifts in this way, stagflation is the theoretical result, and it occurred in many countries in the 1970s and early 1980s, hitting the US and UK particularly hard. This is the supply shock explanation, so called because of its reliance on the aggregate supply curve to explain what happened.
In addition to the oil crises, food prices increased in the early 1970s and there was the Nixon Shock in 1970 when Nixon placed a 90 day freeze on wages and prices and decoupled the value of the dollar from gold (which eventually led to a floating exchange rate for the dollar in 1973 and the end of the Bretton Woods global monetary system). These three issues drove almost all of the inflation between 1972 and 1974. These issues abated in the mid 1970s. In the late 1970s, food prices again began to increase, along with energy and housing prices. Note that the food shock was caused by a large number of factors, including crop failures, corn blight, and El Nino (which among other things, contributed to a then mysterious and economically significant disappearance of anchovies in Peru).
Demand shock
There is another set of explanations that focuses on the demand side. Under this theory, an emphasis is put on the theory that inflation is always caused by an increase in money, probably because money supply had increased (monetary policy) or government spending has increased (fiscal policy). A demand shock or monetary policy explanation for 19070s stagflation exists (note that not all demand shocks are caused by monetary policy). This theory notes that in the early 1970s, there was criticism of the US federal reserve bank (the FED) that monetary policy was too tight in response to the oil shocks. Under this theory, while the oil chocks may have caused some inflation, the following recession was unnecessary if the FED had enacted different policies.
Some push this theory a bit further, claiming that the increases in commodity prices, including oil and food, in the early 1970s was driven by expansionary monetary policies. That is, both the inflation and the recession were caused by the FED - first it was too expansionary in the late 1960s, then to contractionary in the 1970s.
Conclusion
The supply shock explanation gives little room for blame of Carter, as does the fact that stagflation was a global phenomenon. One could blame Carter in some way for some FED decisions and FED appointments, and also blame Carter for his role in global events, whether you are talking about the Iranian Revolution or crop failures, but I don't think such blame makes much sense. Carter was a failed Georgia governor candidate during the 1970 Nixon shock and his role in the 1973-1975 recession as governor of Georgia was very minimal (/s). On the other hand, it is unclear to me exactly how much blame for stagflation to place on Nixon and the 1970 Nixon shock, and I don't think of Nixon (or Ford) as playing a primary role in food and oil prices, but others may disagree.
Carter's policies had little effect on food prices and I'd defer to others on his role in the oil crisis and Iranian Revolution. Similarly, while I have a general understanding that Carter was hard to work with politically and struggled to implement his domestic or foreign agenda, I think it might be a different question for someone else to look at Carter's domestic and fiscal policy. That said, his domestic policy was not wildly different from the other presidents between 1960 and 2000 and is not considered recessionary.
Source:
Blinder, Alan S., and Jeremy B. Rudd. "The supply-shock explanation of the Great Stagflation revisited." The Great Inflation: The rebirth of modern central banking (2013): 119-175.
This paper reviews the broader literature, important papers it reviews include:
Broad focus
Hamilton, James D. "Oil and the macroeconomy since World War II." Journal of political economy 91, no. 2 (1983): 228-248.
Supply shock focus
Blinder, Alan S. "12 The Anatomy of Double-Digit Inflation in the 1970s." Inflation: Causes and effects (1982): 261.
Monetary policy focus
Bernanke, Ben S., Mark Gertler, Mark Watson, Christopher A. Sims, and Benjamin M. Friedman. "Systematic monetary policy and the effects of oil price shocks." Brookings papers on economic activity 1997, no. 1 (1997): 91-157.
Barsky, Robert B., and Lutz Kilian. "Do we really know that oil caused the great stagflation? A monetary alternative." NBER Macroeconomics annual 16 (2001): 137-183.