High oil price cause high inflation?

The president of the Cleveland Federal Reserve Bank said that even the recent oil price increased greatly, the “inflation expectations have stayed well anchored.” She made “a distinction between how much of the pickup has been as a result of energy prices and how much has been translated into permanent inflation.” He also made a conclusion that there might be a quiet inflation in the future, because the high oil prices decrease people’s willingness to buy other goods and services.

I think this is very interesting, other goods and services’ low prices due to low demand crosses out the high inflation. It seems like the market can adjust itself, so can we say that we don’t need to worry about high oil price will cause high inflation?