The Hatters will meet Nottingham Forest in Round 2 after both sides came through midweek replays.
"I was very pleased it was a good professional job and we got the right result," said Blackwell.
"It's handy to be playing Forest in the next round because that will do our bank balance no harm.
"I don't see any reason why we can't make it through to the third round and a big club which given our financial position would be a real bonus."