Sean Raggett's 89th-minute header ensured the National League leaders became the first non-league team to reach the quarter-finals of the competition since 1914.
Dyche felt Burnley lacked quality in attack on a frustrating and, ultimately, humiliating afternoon at Turf Moor, with the Clarets beaten on their home ground for the first time in nine matches.
"It was a day to forget, rather than one to remember and unfortunately there is no positive," he said, as quoted by Burnley's official website.
"The only thing is we played our bit part in a fairytale, but that's not a positive and it isn't to be swept under the carpet; it's to be learned from.
"The fact is it's the first time since I've been at the club when we were really big favourites.
"We haven't experienced that before and it can bring a different feeling in the crowd and a different feeling from the players.
"The real assuredness that comes with growth as a footballer, particularly in the Premier League, is the bit that needs to be added, because we want a future where we are the favourites more often.
"That's what's got to change in our psyche."
Dyche did not make wholesale changes for the match, although three of the back four who held Premier League leaders Chelsea to a draw last weekend were rested.
Nevertheless, he was keen to point out Burnley's priorities this season lie elsewhere.
"The key now is to remember that, of course it would have been nice to go through, but the bigger picture is the league," he added.
"The disappointment is there, but moving forwards we will remind ourselves what the real picture is and that's the Premier League."