Celtic, who look set to come under new ownership, beat Chippa United 2-0 in their Absa Premiership opener at Dr Molemela Stadium.
Komphela replaced Serbian Veselin Jelusic at Phunya Sele Sele in the off-season, having resigned at Chiefs in April shortly before his three-year contract was due to expire.
"I think one we should thank the supporters as always. We are happy that the support has been complemented by the results," Komphela said after Sunday's contest, which was decided via goals either side of the break from Tebogo Potsane and Tshegofatso Mabaso in the City of Roses.
"There were stages where I thought they performed well and played some good football, and also not forgetting that we were playing against a good team Chippa United - a team that keeps possession.
"But also the disclipline from our team, defensively we kept a good shape. I thought on the counter attack we should have scored two more. But we are happy with 2-0 first time at home and a good welcome for me as well."
Komphela is relishing Celtic's underdog tag for their back-to-back matches with Bucs and Amakhosi on August 19 and 29.
"It was crucial that we started with a win. But again, things you don't want to say is that when you play Chiefs, Pirates and Sundowns, logic dictates that the expectations are that they have to win. So it is good to play them because they are not your direct competitors.
"So when you play against them and get a good result it builds your character and helps your confidence. And if the opposite happens, again you say it is okay we have our own competitors, teams of our calibre. When you play Chiefs, Pirates and Sundowns it's easier, when you get the results it is tops."
Celtic's next assignment is a trip to Golden Arrows on Wednesday night.