A 39-4 vote in the Senate on Friday saw Mr Lugo impeached in the wake of a high-profile land dispute scandal.
The United States and Spain have avoided publicly opposing or supporting the move, instead pressing the principle of democracy in Paraguay.
Fernando Lugo’s case was brought before the Senate over his handling of clashes between farmers and police last week in which at least 17 people died.
Vice-President Federico Franco was sworn in as president immediately after proceedings.
President Rafael Correa, the leader of Ecuador, spoke out against the impeachment: “We believe that they [Unasur - Union of South American Nations] should apply the sanctions of what the democratic charter establishes, not to recognize an illegitimate government, even go as far as closing the border.
“Independently of what Unasur decides in respect to the people of Paraguay, in respect to democracy in Paraguay, we won’t recognize the president currently elected.”
The leader of Venezuela, President Hugo Chavez, displayed a similar sentiment: “In the name of the people of Venezuela and in the name of the Venezuelan government and as commander-in-chief, I’ll say it.
“We, the Venezuelan government, the Venezuelan state, do not recognize this illegitimate and illegal government hat has been installed.”
A number of South and Central American governments, including Argentina and Bolivia, have also indicated that they will not recognize the new president’s government.
In both Argentina and Ecuador, Paraguayan and local citizens took to the streets to protest against the impeachment of Fernando Lugo.
Demonstrators gathered outside the Paraguayan embassy in the Ecuadorean capital Quito.
Spain took a more pragmatic approach in commenting on the move.
According to the AFP news agency, a statement from the foreign ministry said: “Spain defends full respect for democratic institutions and the state of law and trusts that Paraguay, in respect for its constitution and international commitments, will manage to handle this political crisis and safeguard the peaceful coexistence of the Paraguayan people.”
The United States took a similar stance.
US State Department spokeswoman Darla Jordan was quoted as saying: “We urge all Paraguayans to act peacefully, with calm and responsibility, in the spirit of Paraguay’s democratic principles.”