The League Two match between Mansfield Town and the Reds on Tuesday at Field Mill was attended by a sold-out crowd and finished in a 0-0 stalemate.
Tomorrow, Wrexham will play Crawley Town on the road, with a sizable home crowd expected at The Broadfield Stadium as well as another sizable away crowd.
Every game at the STóK Cae Ras draws a full house, and according to Parkinson, his players should do well in similar situations when they travel.
“We have worked so hard as a club to get to places like this, better stages for our fans to come and see us,” the manager of the Reds stated.
“It’s crucial that we go into these games with our shoulders back and with joy.
We’ve gone a long way from playing in front of a packed house at Mansfield two years ago when we ran out in front of a thousand people on a Tuesday night in Aldershot.
“We had a sell-out the last two years in the National League when Wrexham were in town, and this is no different.
“We need to retrain ourselves to accept that everywhere we go, there is a cup-tie kind of attitude.
“Every game is going to be like that and we have got to be ready for it.”
Mansfield had the upper hand in the first half, but Wrexham held firm and improved significantly after the interval to earn a tense draw.
Parkinson said Crawley, who is now in fifth place and six points behind leaders Notts County, will have to be ready for another fast start.
“Away games are tough,” he continued.
“All home teams get off to a fast start, so we need to be prepared for it.
“You have to be at the top; you can’t have 6/10 performances.
We have only lost twice this season, so we are doing a good job of adapting.
After picking up a valuable point in a scoreless draw at Mansfield, who are still unbeaten in League Two this year, Phil Parkinson’s team will travel again tomorrow to distant Crawley.
After Tuesday’s second consecutive tie, the Reds, who are currently ninth in the rankings, are two points worse off than fifth-placed Crawley.
It will be another difficult test because the Red Devils have lost more games than Wrexham this year while also recording two more victories.
After Mansfield controlled the first half, Wrexham fought hard to stay in the game. In a much stronger second half performance, the Reds had opportunities to win.
They played well in the final minutes at Field Mill, and if Wrexham can continue where they left off, they will have a decent opportunity of winning three points and capping a very successful trip to two very difficult away games.