Kieran Trippier's fifth-minute free-kick and Danny Ings' fine run and finish just after half an hour saw the Clarets safely through into the third round of the competition.
"We never expected an easy game and we had to work hard," Dyche said.
"In a strange sort of way us scoring early gave Preston a sense of freedom because they had to come out and have a go.
"They did that but our second goal calmed things down a bit although after the break they really stepped onto us and stopped us from playing for a while.
"Then we gathered our thoughts and began to use the ball better as the half went on.
"I think we created enough good quality chances overall to deserve to win the game which is what will happen if you put them away.
"We had a few near-misses and saw one cleared off the line and although we are still a work in progress I was reasonably pleased with the performance.
"It is very difficult to dominate a whole game and you have to find different ways of winning a match."
- Sports & Recreation
- Danny Ings
- Jason Shackell