The Bafana Bafana captain was shot in Vosloorus on Sunday night when visiting his girlfriend Kelly Khumalo, with the South African Police Services setting up a task team in a bid to catch to the killers.
"It is a tragic loss that has left me and the South African football family distraught,” Baxter said on Chiefs' official website.
"Obviously the hardest hit are his family and his friends. On behalf of my technical team, I would like to express our condolences to Senzo’s family, his friends and his club."
The Briton continued: “This act of crime is impacting South Africa negatively. People are calling me from Europe and they are shocked, asking me how I survive working under such circumstances. It saddens me because this is happening in a country where people are warm and nice. Senzo was a good fellow and a fantastic footballer. He still had a lot to give to the nation.
“It was not business as usual at our training this morning [Monday]. We did not have our normal training session. The players are trying at present to come to terms with this sad situation as they were friends and colleagues to the late Senzo. We prayed as a team in memory of Senzo before our training session.
“We hope the family will gather some strength at this traumatic time. I can’t imagine the pain they are going through at the moment.
“May his soul rest in peace!”