Teams like Spain and Argentina had endured rocky opening World Cup matches before going on to win football's showpiece tournament, he said, and it was important his players reflected on the game, learned lessons and moved on.
"We do have to improve. We have to be very self-critical," Martinez said. "Our responsibility here, I think is to assess this match, be self-critical and that's the bottom line ... the World Cup is like that. We continue our work.
"I noticed that the attitude of the players was extraordinary first and foremost, and I do believe in what we can do."
Among the pre-tournament favourites, Portugal made headway inside six minutes through a Joao Neves header but never found their rhythm, despite nearly 70% possession and a team of big names that looked out of sorts, including Cristiano Ronaldo.
It was D.R. Congo who shone in their first World Cup since 1974, soaking up the pressure and levelling in first-half stoppage time when the unmarked Yoane Wissa headed home a cross, sparking wild scenes at the Houston Stadium.
No place for emotion
Martinez said his team started well but the early lead turned out to be counter-productive, with his side playing possession football fruitlessly and showing fear of losing the game instead of trying to win it.
"We scored in a moment where usually the emotions really help out to continue with that momentum and try to score that second goal but it was actually the opposite effect for us," he said.
"We tried to stick to the ball possession, we couldn't make it to the box and we gave an opportunity for Congo to restructure and mount counter-attacks.
"But also we have to learn that our brand of football and our responsibility really is to achieve the highest level possible," he added.
Martinez also warned that the players must not get too excitable when they are leading.
Portugal next play on Tuesday against Uzbekistan, who face Colombia later on Wednesday in the other Group K match.
Martinez heaped praise on D.R. Congo, who he said had a good game plan and played like they were in a big final.
"They were intense, confident. They played like a big final in a big tournament and that shows incredible personality," he said.
"We knew that Congo could do that. It wasn't a surprise."