The two sides will meet again in a replay tomorrow night at The Shay, but Halifax had the better chances in a scrappy game against a Chorley side who had won their previous six home games.
Aspin said: “The most important thing is to be in the draw. I didn’t expect it to be a classic.
“I thought in the first half we were controlling the game, got into some good positions in behind, but our final ball just wasn’t good enough to score.
“I felt we had enough opportunities to get ourselves in front and then in the second half the game didn’t hit any heights and it was one of the games where you’re concerned you don’t get caught on the counter-attack and lose.
“Now we’ve got a chance at home and we’ve got to take that opportunity.”
Ten-man North Ferriby United were victims of a 1-0 giant-killing defeat by Warrington Town after having captain Matt Wilson shown a straight red card in the second half for an off-the-ball incident.
After a cautious start, Ferriby began to get on top towards half time with Tom Denton causing problems up front.
Jamie Yates had an effort cleared off the line and Nathan Jarman’s cross looked as though it might sneak in under the bar before it was tipped over.
But soon after Ferriby were reduced to 10 men, Warrington took the lead with full-back Lewis Field starting and finishing the move.
Ferriby pressed forward and had several chances with Jarman and Liam King going close, but they could not find the net.
Guiseley were unable to match the quality of Grimsby and went out 3-0. They worked hard and contained the home side in the first half, but once Grimsby went ahead there was only going to be one outcome.