Adams joined Saints from Birmingham for £15m at the beginning of July and has already opened his account for the club on debut against Altach on Sunday.
Adkins worked with the striker at Sheffield United and believes he has the ability to excel in the Premier League.
He told theDaily Echo: "I think everybody has to grasp an opportunity that presents itself.
"Che has now got a great opportunity at a super club like Southampton as long as he knuckles down and works hard, who from what I can see have a very good manager.
"There are many young players who have left clubs at an early age and went and played non-league football.
"Che did that which is very good for his development instead of just playing youth football somewhere.
"Like everything you look for natural progression.
"He obviously had a good season last year with Birmingham, scored a lot of goals and caught the club's eye.
"As long as he keeps his mindset right and keeps striving to improve, then he has got a great opportunity from what I can see at a really good football club.
"It's going to be down to him."