A new-look Portugal side that did not include big names like Cristiano Ronaldo, Ricardo Quaresma, Joao Moutinho, Bernardo Silva or Pepe triumphed courtesy of strikes from debutant Helder Costa, Eder and Bruma.
McLeish saw too many similarities in the performance to Scotland's 4-0 loss at home to Belgium in September, with Steven Naismith's 93rd-minute strike providing scant consolation.
"We shoot ourselves in the foot against the two top teams, Belgium and Portugal, with the basic errors that we made. That's the disappointing aspect of it," said McLeish.
"You expect the top teams to cut through you with some majestic skill and leave you trailing but we were the perpetrators of our own mistakes.
"I thought we played well. I thought there was a lot of good football. But we knew we were up against top-class players. I know there was a lot of Portugal players rested but there was still a lot of money on the pitch."
One of McLeish's two wins in charge of Scotland came in their Nations League group, which Israel top with six points.
The manager knows results must improve and remains determined to bring that about.
"For years, every time you lose a game you know there is going to be criticism, you have to take it on the chin and bounce back up," said McLeish.
"We'll do everything we can to qualify next month. We're in that group with Israel and Albania for a reason. It's because of the rankings. I will look at them as cup finals. We want to win the two of them."
Portugal boss Fernando Santos was pleased with the performance from his relatively inexperienced team in Glasgow, but acknowledged it was not a straightforward win.
"It was the first time a lot of these players have played together," said Santos. "There was some anxiety early in the game, lots of running and in the first 15 or 20 minutes it was quite even.
"[Scotland] are great fighters and we were unable to move the ball, from the 25th minute we started to take control of the game. It was a solid display."