Goals from Adam Lallana and Jamie Vardy saw England lead 2-0 entering the final stages of the clash in London, but Iago Aspas halved the deficit in the 89th minute, before Isco levelled the scores in the sixth minute of added time.
Lopetegui has said that his team "showed character, ambition and personality" to turn the game around, in addition to praising Aspas and Ander Herrera, who both made their international debuts.
"The mentality of the team was very good and I think we were the better team by the end of the match. We showed character, ambition and personality to turn the game around. The players were at a good level," Lopetegui told reporters.
"The game had intensity. It was a high-level match, in which both sets of players tried to give it their all. I welcome the debuts of Iago Aspas and Ander Herrera. They played with intensity and took their chances."
Spain are now unbeaten in six fixtures under the leadership of Lopetegui, who replaced Vicente del Bosque as head coach following a disappointing Euro 2016.