With one game to play, the win put Iceland on 19 points, and on the brink of becoming the slammest team to qualify for the World Cup.
Spain, with one more match left to play (against Israel), are the 11th team to secure their spot in the World Cup and the 5th from UEFA.
"As a Spaniard, I don't like the image Spain has shown to the world", Ramos said.
The only downside for Spain was a shaky performance from Gerard Pique, who was booed by large sections of the Alicante crowd every time he touched the ball, after his support for last Sunday's referendum on Catalan independence.
Sergio Busquets and Jordi Alba are the other Catalan players who are key parts of Lopetegui's strongest side, but both avoid the political spotlight.
"Now is the time to focus on positive things, in football and in the country on the whole", Lopetegui told reporters. "But we have to think about the team".More news: Intense Bodycam Footage Shows Las Vegas Officers Responding to Shooting
"Pique's future with the Spanish flag is unacceptable", centre-right newspaper El Mundo complained on Saturday.
Spanish media reported that Ramos admonished Pique when the Spain team met up on Monday although Pique said any talk of ill-feeling with his teammate was untrue, adding that he gets on "phenomenally well" with Ramos and is working on a business project with the Real Madrid defender.
Alba stood up a cross for Koke, who saw his header parried by Berisha as Spain kept the pressure on after the restart, with Rodrigo again thwarted by the Albania goalkeeper after some haphazard defending.
Giampiero Ventura's misfiring Italy limped into the uncertainty of the qualifying playoffs. Most of their players compete in the Champions League and play in Italy.
Thiago Alcantara has attempted 331 passes in the Bundesliga this season.
Click the video at the top of the page to see the mixed reaction to Pique in the win for Spain. We will try to have the best line-up for the match. "Spain have licence to dream again", said Madrid-based sports daily Marca, who also declared the side "The czars of Russian Federation".