Gareth Bale, Cristiano Ronaldo, James Rodriguez and Karim Benzema were on the scoresheet to go with a Marek Suchy own goal as Real cruised to a Group B win.
Sousa said his side got punished for their mistakes, but wants to see the Swiss league champions improve against Ludogorets and Liverpool.
"Of course I'm disappointed for the result because a coach always looks for the best result," he said.
"We need to take another step in this kind of competition. We want to be competitive.
"We were playing against the best team, and the most important players in Europe, and with every mistake you make this team can hurt you.
"We've played against Ludogorets in the past and we want to be competitive against them and against Liverpool."
Basel were unlucky with Suchy's 14th-minute own goal and they found themselves 4-1 down at half-time.
Sousa lamented his team's attitude after going 2-0 down on the half-hour mark.
"We were brave tonight. We had the ball and had chances to score, we showed good character but we were too naive sometimes," he said.
"When there is too much space between lines you must choose the best decisions because if you don't you are going to suffer.
"The gaps in our teams were too large sometimes and that made Madrid counter-attacks possible. The team mentality began to fail after the two first goals."
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