Gallagher wants the club to succeed for their own sake and reach the Europa League third qualifying round.
But he also believes progress is important for the country as a whole.
He said: “Scottish football gets a lot of criticism and the further that the likes of ourselves, Aberdeen and Rangers and Celtic can go the better it is for Scottish football as a whole.
“You want to take pride in doing well for your club but for your country as well.”
Many ‘experts’ will have Well down to go through after disposing of another Northern Ireland side, Glentoran, in the last round.
But Gallagher will take nothing for granted against former St Mirren boss Oran Kearney’s side who put out Slovenian Champions League regulars Maribor in the last round.
Gallagher told the Times and Speaker: “You have to give anyone that’s in the Europa League respect. It’s a massive competition and they’ve proved that they can do it, they’re not there to make up the numbers.
“Maribor were probably one of the most favoured teams to reach the group stages so to put them out away from home shows they are a well organised side and a good team and we’re going to have to be right on our game and right up for it.”
Well are at least heading across the Irish Sea on the back of a win - their first in the league this season - after beating St Johnstone.
Gallagher admitted: “The longer it goes without the win you do start to put a bit of unwanted pressure on yourself.
“Funnily enough the games we’ve got anything from we’ve probably had less possession. Last season we played a lot on the counter attack; teams came out and tried to press us.
“This year teams are giving us the respect of the likes of Celtic and Rangers; they’re just sitting in their own half and letting us have the ball and that’s changed our dynamics a wee bit.”