Van Dijk was forced off, and Liverpool confirmed on Sunday that the centre-back would require surgery to repair anterior cruciate ligament damage.
It is anticipated that the Netherlands defender could miss between six and nine months of action as a result.
“This afternoon I met with a leading consultant to start the process of planning the finer details of my rehabilitation following the incident yesterday,” Van Dijk wrote on social media on Sunday.
“I’m now fully focussed on my recovery and will do everything I can to be back as quickly as possible.
“Despite the obvious disappointment, I’m a firm believer that within difficulty lies opportunity and with God’s help I’m going to make sure I return better, fitter and stronger than ever before.
“In football, as in life, I believe everything happens for a reason and it’s important to try and keep level headed whether going through the highs or the lows.
“With the support of my wife, kids, family and everyone at Liverpool, I’m ready for the challenge ahead.
“I’d like to thank everyone for the messages of support, it’s meant a huge amount to me and my family, and I’ll now be doing everything possible to support my teammates in any way I can ahead of a big few weeks ahead as I take my own recovery day by day.
“I’ll be back.”
Club sources are reluctant to rule out a return to action this season for the 29-year-old, who had played every minute of the 74 league games prior to being forced off the pitch on Saturday, a spell stretching back to his substitution in the 3-0 home win over Southampton in September 2018.