Bolton, a prominent hardliner in Washington's attempt to pressure Venezuelan strongman President Nicolas Maduro from power, was sacked Tuesday.
This sparked speculation in some media outlets that Trump might seek a more conciliatory line.
However, the president indicated on Twitter that his policies could instead harden.
"In fact, my views on Venezuela, and especially Cuba, were far stronger than those of John Bolton. He was holding me back!" he said.
The United States already imposes sanctions on Venezuelan officials and its oil industry.
Washington has also recognized opposition leader Juan Guaido as the legitimate president, but with little success in shifting Maduro's grip on power.
Millions of Venezuelans have left the country as a result of political unrest and economic collapse, with food and medicinal supplies often scarce.
More than 50 countries recognize Guaido. However, Maduro still enjoys support from Russia, China and Cuba.