Baena opened the scoring from the penalty spot in the 39th minute after a handball by Lukáš Ambros. Pubill then settled the contest with a stoppage-time finish, scoring in the 96th minute after Czechia had been reduced to 10 men following Ladislav Krejčí's dismissal.
“It has been a very closely contested match against a very intense team,” De la Fuente said afterwards. “When we have been able to play with more calm, we have wanted to attack quickly. If we had scored earlier, it would have been easier.”
The Spain coach acknowledged that the hosts had made life difficult, particularly from set-pieces.
“They created danger for us from set-pieces. I think we played with great composure, control and awareness,” he said.
The result moved Spain to 15 points from five matches in Nations League Group A3, while taking them beyond Brazil's previous unbeaten sequence.
“Intelligent people recognise the value of what is being achieved. We have surpassed Brazil's run. Only a fool would fail to appreciate this,” De la Fuente said.
“After 44 matches without losing, defeat is getting closer. We are aware of how difficult this is.”
The coach also expressed frustration with reports surrounding the national team, insisting that criticism was not his concern but that inaccurate stories were unacceptable.
“What upset me was that they were not telling the truth, that they were inventing situations to generate a story,” he said. “I only ask for respect.”
There was positive news regarding the squad, with De la Fuente confirming that Lamine Yamal and Mikel Oyarzabal would join the group ahead of Sunday's meeting with England.
“We have very good news. Both of them are going to join the squad. Both Lamine and Oyarzabal,” he announced.
He also praised Fermín López's contribution, despite the midfielder still waiting for his first Spain goal.
“Fermín is a fantastic footballer who gives us so much. I have found out today that he hasn't scored for us,” De la Fuente said. “I focus on everything he creates. The goals will come, but scoring is not essential for him to be important to us.”