A visibly distraught Solinas made the appeal after his side, in fifth spot on the Absa Premiership log, lost 2-1 to Orlando Pirates in the Telkom Knockout semi-finals at Durban's Moses Mabhida Stadium on Saturday.
Amakhosi's third straight Soweto Derby defeat in 2018 ended any immediate hopes of ending their unprecedented trophy drought, which is into its fourth season.
However, Solinas, who arrived at Naturena in July, is adamant he can bring back the glory days to the Glamour Boys.
The Italian will naturally be hoping for a morale-boosting win in their CAF Confederation Cup opener with Zimamoto of Zanzibar at Nelson Mandela Bay Stadium in Port Elizabeth on Wednesday.
"I believe we can change the situation. Maybe we need the time, but we can change it," Solinas said.
"We have our plan for the market. Me, I want to say to our supporters, please guys, don't abandon Kaizer Chiefs and continue believing in Kaizer Chiefs. I'm sure in the future Kaizer Chiefs will not disappoint our fans.
"We have our project to reinforce the team, to turn Kaizer Chiefs to be more strong. We need time. Me, I'll never give us. From now onwards I'll work hard to improve. Me, I work hard, guys. Me, every day I work 10 hours. Maybe it's not enough, maybe I'll have to work 11, 12 hours. But me I'll never give up. I want to improve, fighting, this is my spirit, this is my hope.
"Me, I take responsibility hey. Don't worry, I take responsibility. I put my face with the fans, with the media. This is my face, this is my responsibility. Me, I'll continue to work hard for Kaizer Chiefs, for this badge (touching it) because this is a very big club. The best club in South Africa, one of the best on the African continent. Me, I will work hard."