Still, Moyes will be comforted by the performance of 17-year-old trio Seamus Coleman, Shane Duffy and Jose Baxter, who all played their part in an impressive win in dreadful conditions in Athens.
"Tonight was a case of needs must and I think the spirit of Everton was apparent among both the younger and more experienced players," said Moyes.
"The young players who came in did really well and I'm delighted with them.
"And Tony Hibbert, again playing out of position at centre-back, did a great job. They all worked so hard to get the result, it shows there is a heartbeat at the football club and hopefully we can kick on from here and improve."
Moyes admitted qualifying with a game to spare enables him to field a weakened team in the last group match against BATE as he looks to get some of his walking wounded back to fitness.
"It's very important to have qualified with a game to spare as it gives us a week where we don't need to be too intense with the squad," he said.
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