Spain's head coach Vincente del Bosque has criticised his team for letting Ukraine "control the game" and has warned that they must improve.
The former European champions beat their Group C opponents 1-0, courtesy of Alvaro Morata's debut goal for the national side.
However, Del Bosque was unhappy with his side's second-half performance and insists that they must improve before their game with the Netherlands on Tuesday.
"We played well in the first half and created chances but we struggled to put them away. Later, in the second half we brought on Juanfran and [Santi] Cazorla but still found it hard to score," the 64-year-old told reporters.
"We dropped in intensity and allowed them to control the game. Our second-half performance left a bad taste in the mouth. We've got to start improving.
"Everyone played well. We've got three points; the only downside was the second half. We'll be making changes for the Netherlands game on Tuesday because some of the players need a rest."
Spain are second in Group C, three points behind Slovakia who have won five out of five of their qualifying matches.