The Toffees won 4-3 on spot-kicks after stunning the holders with a 119th-minute equaliser just as it looked as if their Wembley dream had died for another year.
The Everton boss said: "You just have to prod people sometimes, and they needed a good prodding. But they didn't half respond, and if anybody doubted them last week they should eat their words because they were top-notch this week.
"This is Chelsea's first defeat in the cup in nearly three years, so I have to praise the players - they were immense throughout. The goalkeeper made two or three brilliant saves, which we needed."
Moyes added: "I said last week that if we had beaten Bolton, I think we would've gone eighth in the Premier League.
"The manager and the players had a chance to change the perception of the club and we didn't do it. Not only that, we didn't play well. I hope here we're able to send 6,000 home with a much better feeling about our team and our club."
Source: PA
Source: PA