The League Two Sulphurites played out a 2-2 draw with a youthful Reds side at Wetherby Road in what was their fourth friendly of the summer.
Leading through new signing Max Wright's tidy one-on-one finish after a quarter of an hour, Simon Weaver's men had good chances to add to their tally before being pegged back by Aiden Marsh's strike late in the first half.
Jasper Moon was then able to nod Barnsley in front from a left-wing corner before Pattison burst through on goal and slotted home a 72nd-minute leveller.
And although he believes that there was plenty to be positive about performance-wise, the former Middlesbrough midfielder feels that the kind of defensive lapses which became a feature of Town's underwhelming 2021/22 campaign again proved costly and need "nipping in the bud".
He told the Harrogate Advertiser: "I thought that the performance was very good.
"It's a lot better testing ourselves against higher-division opposition rather than going and steamrollering lower-league opposition. You want to be playing against good players because it stands you in good stead when the season kicks-off.
"And I thought that we were good for the majority of the game, but just two moments have cost us and we've conceded two goals and ended up drawing 2-2.
"Realistically, we could have won by two or three. It could have been a comfortable win, but it's just those two moments, which happened a lot last season.
"We are trying to nip it in the bud. The only positive I could maybe find in that is that we're hopefully getting them out of the way now before the season starts and nipping it in the bud now."
Pattison looked set to register his goal of pre-season four minutes before he eventually did, having been played through on goal by Luke Armstrong and beaten Barnsley custodian Jack Walton, only to see his finish hit the inside of an upright and bounce to safety.
And, while he was pleased to find the back of the net soon afterwards, he says that he remains disappointed not to have finished the match with a brace to his name.
"I was buzzing to get off the mark, it is always nice to score and hopefully I can keep them coming when the season starts next Saturday," the 24-year-old added.
"It's obviously good to get in the positions but I want to be taking my chances as well. The first one where I've hit the post, if I missed that in the league I would be fuming.
"So, I've got to do better. I'm getting in the right positions, but it is about finishing them off."
Wednesday night's result means that Town have now won one, drawn one and lost two of their four friendly fixtures to date, scoring three goals and conceding seven in the process.
They wrap up their pre-season campaign this Saturday when they visit National League Gateshead, 3pm kick-off.