The Ammies survived a scare from their hosts to eventually run out 2-1 winners and are now in the hat for Monday's first round draw.
Speaking to the club's YouTube channel after the game, Alexander said getting through was the main objective.
"I spoke in the week about what a tough fixture it could be and that proved to be the case," he said.
"They were organised and focused on what they had to do and they made it a tough game for us so credit to them.
"It was a good cup tie - the job today was to get through to the next round and we've done that and we're really pleased with that.
"We missed some good chances second-half but we're delighted we've come here and got the job done and that's the most important thing."
Salford will be ball '59' in Monday's FA Cup First Round draw.
PHOTO BY CHARLOTTE TATTERSALL