Gallagher started the Ibrox club's first pre-season friendly against Buckie Thistle on Thursday night - and scored two goals in a comfortable 3-0 victory.
The 19-year-old broke through in the second half of last season and looks set to be a regular starter in Ally McCoist's team in the 2014/15 campaign.
Promising midfielder Charlie Telfer turned down the offer of a new contract as he was apparently disappointed at his lack of first team action at Rangers.
The signings of Kris Boyd and Kenny Miller has led to growing accusations that McCoist does not put his faith in kids.
But Gallagher has dismissed those claims, saying: "The manager played a lot of the young players the other night in our pre-season friendly against Buckie and I think that goes to show the mentality he has.
"I know there has been a lot of criticism over the summer about the young players at Rangers.
"But if you are good enough it is not an issue how old you are.
"You just need to get your head down, work as hard as you can and prove your worth.
"The chances are there and you have got to take them when they come.
"There was a lot of attention on Charlie Telfer's move. I think that maybe resulted in some criticism about the club and their development of youth players.
"But the chances are definitely there for you. If you are good enough and you work hard enough then the chances will come your way."
Gallagher was set up for his second goal at Victoria Park by Barrie McKay.
And he predicted the Rangers winger will be one of the stars of the new season.
McKay, who was the stand-out performer for Rangers in Moray, was loaned out to Morton last season and he appears to have benefited from his time in the SPFL Championship with the Cappielow club, despite their relegation to League One.
Gallagher said: "Barrie was excellent against Buckie. I was with him a couple of times over the summer and he has kept himself really fit.
"He has done a lot of work away from Murray Park.
"He has done himself justice to come back as fresh and as sharp as he is looking and I am sure he will kick on from here and have an excellent season.
"The manager had a word with him at half-time and told him how bright he looked.
"I am sure he will be looking to press on from here and I am sure he will do it.
"I think that by playing in the Championship he will know what to expect this year.
"He will relish it. He is that kind of player, he just loves playing football.
"He will be looking forward to the start of the season."