Following his first competitive appearance for the club in a 5-0 cup win at Burton Albion last week, the centre-back maintained his starting role for the trip to White Hart Lane on Saturday afternoon and exerted himself well.
The Cameroon international helped keep Spurs strikers Harry Kane and substitute Vincent Janssen quiet across a fine performance, although James Milner's penalty was cancelled out by Danny Rose to deny Jürgen Klopp's men the three points their display deserved.
Defender hoping to kick on after first league display
The 25-year-old, who was on the bench for the Reds' first two league games as he recovered from an ankle injury, explained to Liverpoolfc.com that his first league run-out was "very intense" but called it "nice to play 90 minutes."
Matip said that the beginning of his season "was not so easy" with his injury and therefore insisted it was "good to play" as he declared that his fitness and form "will get better."
He praised his defensive partner Dejan Lovren, saying that he "always covered me" and "gave me help" before adding: "I also tried to help him but it was very difficult because it was an intense game. But we can continue and next time maybe we'll win."
Start to the season could've been better, admits Matip
The draw means Liverpool have taken four points from an available nine to the start the 2016-17 season going into the first international break, the point in north London following a win at Arsenal and defeat to Burnley.
Matip, who only joined the club on a free transfer from Schalke in the summer, admitted that their start "could have been a little bit better" and "especially" so at Spurs, where he suggested they could - and should - have won.
"We were in front for a long time, but in the end we only got one goal," acknowledged Matip, who said that they must "work with this point" and looking forward to playing "at home" against Leicester City where they "want to take three points."
The Reds' No.5 will hope his debut impressed Klopp enough to be able to maintain his place in the starting eleven for their first Anfield fixture at home to the champions next month.
He also earned praise from teammate Simon Mignolet, who hailed Matip as "outstanding" and lauded his "physical presence" as making "a big difference" at the back.