Jordi Alba's own goal in just the second minute eventually gave Sociedad victory in San Sebastian as they held on against Barcelona.
Moyes compared the feeling in the lead-up to Sunday's clash to his time with Everton in the Premier League, claiming that it is difficult to spot weaknesses with Barcelona.
"The win feels similar to the early days at Everton," he said at his post-match media conference.
"How was I ever going to get a result against the likes of Arsenal, Liverpool, Man United at that time?"
The Scot added: "We've talked about Barcelona at my past clubs, at Everton and at Manchester United. I've watched them with admiration and we used to wonder how to possibly get a result against them.
"Tonight I had the opportunity. It was a long night, we scored early and I would like to have given them a harder game. We did make it very difficult for them, though.
"I would like to be competing against Barca, Real Madrid, Atletico, Valencia and Sevilla at the top of the league. To do that we have to make the squad stronger."
Barcelona had 69 per cent possession at the Estadio Municipal de Anoeta, while the visitors took 12 shots to Sociedad's five, prompting Moyes to praise his defenders.
"We worked hard defensively and defending is a big part of football," he said.
"You don't win games if you don't defend well. The way that we played at the back gave us the chance to win this game."
The victory saw Sociedad move up three positions to 13th in La Liga with 18 points, while Barca missed the chance to overhaul Real Madrid - who lost 2-1 at Valencia - at the top of the table.
That missed opportunity prompted criticism of Barcelona coach Luis Enrique, who chose to start Lionel Messi and Neymar on the bench, but Moyes backed the decision of his counterpart from the Catalan capital.
"I expected Neymar and Messi to maybe be on the bench," Moyes said.
"I've managed a very big club, you have a big squad and a lot of games. The big games come later for these teams - April time - and you have to give the big players rest to keep them fresh for then.
"I thought Luis Enrique made the right decision and the players that played tonight are really good players. He knows his squad the best and in his position I would probably have done the same thing."
