Blackpool manager Neil Critchley admitted his side had to “work extremely hard” before seeing off non-league Eastbourne Borough 3-0.
The League One side had to wait until the 58th minute before making the breakthrough against the National League South outfit in their FA Cup first-round tie.
Critchley said: “Obviously delighted to win, but we were made to work extremely hard for it. Eastbourne made it difficult for us in the way they set up.
“The longer it stays 0-0 you always think it only takes one opportunity and it can change the game.
“We missed chances and the longer it stays like that you’re thinking it might not be your day. Fortunately we got the breakthrough and then scored a second quite soon after.
“I was disappointed with our performance after that for the last 15, 20 minutes, but we’ve scored three goals away from home, kept a clean sheet and are in the hat for the next round.”
Gary Madine opened the scoring and doubled the lead 10 minutes later before Jerry Yates grabbed a late third.
Eastbourne manager Danny Bloor said: “I think our football club and players can be very proud of the display we put on against a very good side.
“Gary Madine, a player with Premier League experience, I felt was the difference between the two sides and we can be proud of our performance, especially keeping them to 0-0 at half-time.
“You’re never happy when you lose, but when you play a Football League side you have to be realistic, albeit 3-0 perhaps flattered them a little. We have to take the positives from the game.
“We have a lot to take forward into our National League South campaign.”