Thorgan Hazard scored a stunning goal but Belgium needed to defend doggedly and ride their luck under heavy pressure late on to hang on for a 1-0 victory in Seville on Sunday.
Coach Martinez said: “It wasn’t just about how good we could be, it was about how we could adapt to what Portugal do the best, which is do exactly what they need to do to win.
“That is why they are the current champions and winners of Nations League. They have incredible experience and know how to take those moments to hurt you.
“We had incredible concentration and defended really well. We scored a very good goal.
“In the second half the more the momentum went to Portugal we had to show an incredible mentality. Everything was about being disciplined and tactically astute.
“We never lost concentration and there were difficult moments. The way Portugal pushed for victory until the end, this gives me incredible satisfaction.
“This is what a winning team needs. We know the talent we we have but all the other elements you need were shown today. For us it was the biggest test there is.”
Belgium will now play Italy in the last eight on Friday.
Before that they face an anxious wait to discover the extent of injuries suffered by key pair Kevin De Bruyne and Eden Hazaard.
De Bruyne missed most of the second half after picking up an ankle injury in a challenge from Joao Palhinha and Hazard sustained a muscular problem late on.
“We are going to need 48 hours to find out the extent of the injuries,” Martinez said. “We will go back to Belgium and make the scans tomorrow.”
Portugal coach Fernando Santos felt defeat was undeserved.
Santos said: “I think it is unfair but this is football. If you score you win – they scored, we didn’t.
“But apart form the first 10 minutes when we didn’t play that well, my players played with a strong mentality and tried to attack.
“We wanted the ball. We had 29 shots and couldn’t score one. They had six shots and one on target and they won.
“We hit the post and carried on being dangerous but the ball wouldn’t go in. We kept our heads up and kept thinking we could turn things but this is football. Sometimes we have had fewer chances and won.
“We are very disappointed. We thought we could reach the final and win – that was our attitude. Some of the lads are crying in the changing rooms but we can still win more titles and now we are looking forward to the World Cup.”