The Dutchman was banished from the field of play just before the half-hour mark at St James' Park last month, having committed a last-man foul on Alexander Isak.
Rather than immediately trudge off the field, Van Dijk launched a foul-mouthed tirade on referee John Brooks and ultimately had to be ushered down the tunnel by Jurgen Klopp.
The Reds remarkably came from behind to win 2-1 on the day thanks to a Darwin Nunez double, but Van Dijk was charged with improper conduct two days after the match.
Having now admitted to using abusive and insulting language towards the officials, Van Dijk has been hit with an extra one-game ban as well as a hefty fine of £100,000 - a decision which the 32-year-old concedes he can have no qualms over.
"Following the announcement today I'd just like to make clear I totally accept the panel's decision. It was the first red card of my Liverpool career and I let my frustrations get the better of me in an intense and heated moment," Van Dijk said on social media.
"I apologised immediately after the game to the match officials and take full responsibility. Time to move forward now. I will continue supporting the team in every way I can."
Liverpool had to make do without both of their first-choice centre-backs for the visit of Aston Villa last weekend, as Van Dijk's suspension coincided with an injury to Ibrahima Konate.
The Frenchman's hamstring problem had already ruled him out of the showdown with Newcastle, where Joel Matip filled in at the back, and he was joined by Joe Gomez in a second-choice centre-back partnership against Unai Emery's side.
Despite the absence of their leading defenders, Liverpool kept a clean sheet for the first time this season in a 3-0 beating of the Lions, thereby moving on to 10 points from their opening four Premier League fixtures.
However, Liverpool will now be forced to cope without Van Dijk once again for their showdown with Wolverhampton Wanderers after the international break, while Konate's availability is also unclear.
The 24-year-old was due to represent France in their September clashes with the Republic of Ireland and Germany, but he failed to overcome his hamstring injury in time and was replaced by Nice's Jean-Clair Todibo.
Liverpool were unable to bring in another centre-back during the final knockings of the summer transfer window, instead prioritising their midfield rejig with the captures of Wataru Endo, Dominik Szoboszlai, Alexis Mac Allister and Ryan Gravenberch.
However, Japan international Endo has previously filled in as a centre-back, while 20-year-old academy product Jarell Quansah has already made two Premier League appearances off the bench this season.