Barker, who has returned from injury quicker than expected, grabbed the clincher for Steven Gerrard’s side to ensure they go into the international break on a high.
Speaking to RangersTV at full-time, Barker said: "I have always been a birthday man! I love birthdays and I always go the extra mile on other people's birthdays so it is nice for mine today.
"To get a goal is a special feeling.
"I feel good and long may it continue.
"Someone mentioned before maybe last year we wouldn't have won those types of games and this year we are winning them.
"The main focus is to get the three points every game but the way we did it today, it wasn't us at our best but we have a massive game in two weeks' time and we are all focused on that now.
"This is our home and we don't want anyone to come here and take points away from us - we have always been like that - it is an unbelievable stadium with unbelievable fans, and if someone is going to come and take it, they have to really earn it and at the moment, we are not letting teams do that."
Gers’ players not on international duty will enjoy something of a break off the back of a hectic fixture schedule before the Old Firm game in just under a fortnight.
Barker would love nothing more than to be named in the XI for that one and added: "It would be massive. Off the back of a season where I didn't play much football, this season, I have got my head down and I have been in the team.
"It's a massive game, but it is the same as every other game."