The 18-year-old striker signed his first professional contract earlier this week after impressing in the reserves this season.
In seven appearances, five of which have been starts, Baker has netted four goals to earn what Parkinson insists is a deserved step up to the first team squad along with Louie Swain and Forrayah Bass.
The City manager said: “Adam is in the squad on merit, while the others I want to give a chance to experience what it is like to go away with the first team.
“It is a ‘well done’ for all the lads. We have a great School of Excellence that is run by Peter Horne and I believe it is important the young lads are shown that there is a route through to the first team.
“Bringing through your own players is vital for any club and particularly ones at our level.”
City, who banished any threat of relegation by beating Macclesfield last week, face a tough final two games with today’s trip to promotion-chasing Cheltenham Town being followed by a home encounter with leaders Swindon.
Parkinson added: “We have had decent results lately and we want to keep that going. It won’t be easy as Cheltenham have had a great season under Mark Yates, while Swindon have been at the top for a long time. We want to finish on a high and then start building towards next season.
“We all want to do a lot better next season but that can only happen if we get it right now. We had a board meeting on Thursday to discuss the way forward.”