Burnley won it with first half goals from Kieran Trippier and Danny Ings but Grayson thought it was his team in the ascendancy as both goals were scored.
He said after the game: "We dominated possession for large parts of the game; their keeper made some good saves and we limited them to very few opportunities. The goals we gave away were scruffy goals and ones we could have prevented, but we passed the ball with purpose, we closed down and worked hard and that is a testament to the players that they reacted in the way I wanted them to after the weekend.
"Both goals came against the run of play. Stucky (Thorsten Stuckmann) probably feels he could have done better with the first and the second came after we got on top and then in the second half we were the dominant team.
"We got the ball into the right areas and on another day we could quite easily have got something from that game, the scoreline wasn't a true reflection of the game.
"I reiterated to the players at half time that if we could get one, we could have gone on to win the game, but we just couldn't get that one to get us back into the game. But the players stuck at it; put Burnley under a lot of pressure and their goalkeeper made some great saves."
Dyche, though, felt the Clarets were deserving of the win overall. "You have to find a way to win and we have done that again tonight," he said as we moved into the next round.
"I thought the lads mostly delivered a good performance. We've played patches of really good, productive football and stayed strong when we haven't kept the ball as well, but despite being patchy at times, the moments of quality turned it in our favour.
"There was a spell in the second half where I didn't feel we kept the ball, but give Preston credit because being 2-0 down brought them a lot of freedom. They pressed and lost any inhibition, got on the front foot and pressed us all over the pitch.
"That, in turn, made us go longer at times and made life difficult, but as the game wore on I felt we took control of it again and kept the ball better.
"Overall we've done the job. It was a local derby against a good club with a good manager and good players. I think they will be a force this season in their division, so I am very happy with the outcome."
He had to make one change tonight with goalkeeper Tom Heaton suspended and replaced by Alex Cisak, but he also took the opportunity to give David Edgar his first start of the season and fit again Michael Duff and Ben Mee their first appearances.
He explained: "It was important to get players up and running and the only way to do that is to play first team games at some point. The changes were made with that in mind and we are happy they came through unscathed and fit and well."