The Reds were open to selling Phillips in the recently concluded transfer window, but no move materialised for him before Tuesday’s deadline.
With the centre-back looking likely to remain at the club, Liverpool took a U-turn on the last day of the transfer window and offered him a new long-term contract at the club.
Liverpool legend Houghton has stressed that having signed a new deal, Phillips now have to trust in himself and try to earn some game time under Klopp as the season progresses.
Asked about his thoughts on Phillips signing a new deal at Liverpool, Houghton told LFC TV: “You have to back yourself.
“If you have got confidence in your ability, then you have got to say to the manager look, ‘I do not think it is right for me to move on at the minute, I am trying to prove you wrong, give me the opportunity.
“Do not shut your mind off to me not getting in the team.’”
Houghton, who acknowledged that Phillips raised his game as he started to play more senior games for Reds last season, added that if he is not needed at Liverpool, then he can always look for a loan exit when the window swings open next time.
“When we have seen Nat Phillips last season, maybe at the start it was something new for him, and he struggled a little bit.
“But the more games he played, he got up to the speed of playing in the first team football and probably warranted an opportunity and he was happy enough to take it.
“I am sure if he is not needed, he will go out on loan somewhere and get some game time that way.
“But the manager still keeps his eye on him, because he knows what he can do, he has shown what he is all about as a player last season.”
Phillips is yet to make a matchday squad this season as he is down the pecking order at the club with the senior centre-backs all being fit, while new boy Ibrahima Konate is also providing an additional option in that position.
