Neither side managed to register a shot on target in a lacklustre regulation 90 minutes, but Ivan Perisic hit the upright with a header in the second half of the additional period.
Portugal gathered possession from there and raced up the other end, with Ricardo Quaresma heading home after Croatia goalkeeper Danijel Subasic denied Cristiano Ronaldo in the 117th minute to set up a quarter-final against Poland.
Santos confessed he would have liked to have seen his team play a more coherent, fluid game in the final third, but acknowledged that will not always secure you the win.
"It was a very tactical match, we tried to take over but Croatia didn't let us. But we didn't let them, either. You must look at both sides of the coin," he said in his post-match media conference.
"We faced an amazing team, they've played some of the best football in the group stages. They always try to play their type of football.
"We were prepared for that, I got the team ready to fight against that and take advantage of their weak spots. We didn't let them counter-attack much, we paid special attention to that.
"We sometimes played well in attack but I believe we have to improve. In the first half, we had a plan to make the most of the times that the full-backs got forward.
"Sometimes I think we should have passed the ball faster, that didn't work out as we wanted, but we should congratulate Croatia, they didn't let us play as we wanted.
"This was a final, and we won. Today we were the lucky ones. But I think it was fair. We have a very hard match against Poland and we must prepare for that now. We'd like to play a pretty game but that's not always how you win tournaments."
Nani, who played a role in the winning goal, made his 100th appearance for his country - the fourth player to reach the milestone after Ronaldo, Luis Figo and Fernando Couto.
Santos was proud of the forward, but also all of his players for their display.
"It's always a beautiful number to reach, I'm very happy with Nani and with all the players. They showed a lot of commitment," he added.