Midfielder Dickson, 18, was hugely impressive after coming on as a 55th minute substitute, while 16-year-old defender King was effective after replacing captain James Tavernier at right-back for the closing 20 minutes.
“I will be watching them both very closely now,” said Gerrard. “I want to see how they react to that taste of first team football and see them work hard to get more opportunities.
“I’ll be watching to see if it goes to their head or they want to really see it as a start of their careers going forward.
“They both look physically ready. You judge them in training first and foremost - they are training like first team players, not kids coming in to make the numbers up.
“I see a lot in the academy from afar and these are two good types who deserved the opportunity today.”
Gerrard revealed boyhood Rangers fan Dickson reminds him of himself when he was looking to force his way into the Liverpool first team at the start of his illustrious playing career.
“I thought young Dickson was terrific,” said Gerrard. “He played with energy, personality and character. He’s the type who will never let me down.
“He’s probably had a similar upbringing to myself in that he knows what it means to represent Rangers and the shirt.”