It's only the third time the Hampshire club have reached the third round stage since reforming in 1992.
And the boss believes a big day in the spotlight is nothing less than their loyal fans deserve.
"What we have to understand is, they are from a different stratosphere," Widdrington says. "Size of club, size of following - these have won the FA Cup five times.
"We understand that. But it's a reward for the players getting there, in one respect. It's also redemption for the people who have supported Aldershot for a long time and seen the phoenix club come back.
"It's been explained to me by my bosses the last four or five years haven't been great in terms of results. This season they have been good but I think, moreover, people have enjoyed the way we've taken the game to most opposition.
"If we can do that at times at West Brom then we will do that. I'm not going to park a bus."
They certainly haven't done that so far. Although they conceded four late on, the swashbuckling Shots led 7-0 against League Two Swindon Town in the first round.
They then beat Stockport County 1-0 in a replay after a 2-2 draw in the first game.
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