The forward bagged one of his side's two goals in the 2-0 win over Bournemouth on Sunday.
The attacking midfielder was a surprise starter Sunday’s win over Bournemouth, with Arsene Wenger choosing him ahead of Theo Walcott in his starting 11.
He justified that decision fully, scoring the second goal of the game to help his side to a much needed 2-0 victory.
That goal was his first ever away goal for the Gunners since joining in 2011, while it was his first goal for the club in over 18 months.
And Souness says he must improve his goal tally significantly in future if he is to progress and become the top player his potential had suggested he would be.
“It’s a good finish from Oxlade-Chamberlain, but we’ve got to see more of it from him,” he told Sky Sports.
“If he’s going to progress and be a proper player, he’s got to be scoring more goals.”
“His stats tell you that he’s got to get more goals. As a manager or supporter, you expect an attacking midfielder to be getting more goals.”
Oxlade-Chamberlain will now be hoping for extended game time in the Arsenal first team to prove his worth to the squad.
He has struggled with injuries in recent years, with a series of niggling problems having seriously hampered his playing time.
Now he is back fit though, he is in contention once again, and will be hoping that he can build upon his goal on Sunday to enjoy a strong end to the season as the Gunners eye the title.