The Red Devils scored first through Patrice Evra in their Champions League quarter-final second leg against Bayern Munich before conceding immediately to Mario Mandzukic and then allowing Thomas Muller and Arjen Robben to settle the tie.
United lost 3-1 on the night and 4-2 on aggregate to bow out of Europe's top competition and Moyes felt it was the mistake that led to Bayern's leveller which really killed the spirit of his team.
"I am pleased with their (the players') performance, but a couple of small errors cost us in the end," he told reporters.
"The 30 seconds after we scored the first goal is poor, as a schoolboy you are told not to concede a goal straight away after scoring.
"We conceded too quickly. It's always going to be tough, but after the first goal you need to give five or 10 minutes (without conceding).
"I don't know if the concentration went after the goal, but we had enough experience on the pitch to do that.
"I never thought we were out of the game, we needed to score one more goal but obviously the third one killed us."
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