George Nkencho, 27, died in the incident outside his Dublin home in December.
His sister said his death was untimely, unplanned and unwanted.
Gloria Nkencho delivered a eulogy at the start of her brother’s funeral Mass at the Sacred Heart of Jesus Church in the capital on Saturday.
She said: “This is in memory of my brother, for everything he stood for, for all that he believed in.
“It was untimely, unplanned and unwanted, but he is welcomed into the bosom of the Lord.
“He is at peace, he is happy, my family will be at peace.”
Mr Nkencho was shot multiple times outside his home in Clonee, west Dublin.
He was allegedly brandishing a knife and threatened gardai before he was shot by members of Blanchardstown garda armed support unit.
Mr Nkencho was suffering from mental health issues at the time.
His sister said: “Remember George for not what they said about him, but for who he is and for who he will forever be in our hearts.
“A brother, a son, a nephew, a best friend, a cousin, a team-mate, a classmate, a partner.
“He is at peace and we love you.”
The cleric who conducted the service said: “Let the law do its work as investigations are still ongoing.
“Be patient with the appropriate authorities, that is the only advice I will give to the whole family.”
The funeral was attended by just ten people in line with Covid-19 rules while about 100 friends and neighbours gathered outside the church.
Some held posters in his memory, including Black Lives Matter.
Another displayed his image and said: “Farewell George – we won’t forget, we’ll stand for justice and truth.”
The hearse carried a picture of the victim alongside his coffin. A CD, a flag and notebook were placed on the white coffin by members of Mr Nkencho’s family.
The priest said: “A sudden death of a loved one is like an unexpected power outage, it changes our lives in the blink of an eye and turns our lives upside down.
“I know you all feel the same way and are devastated by George’s death.
“Natural death is not easy to accept – how much more a tragic (one).
“Words may not be adequate to express the pain and sorrow we feel as a parish community, our hearts are broken at this time.”
He said the gift of life was fragile and precious.
“It is our hope that we live to attain old age but this is not guaranteed.
“When death comes as a tragedy it robs us of aspiration, it breaks our hearts and robs us of joy.
“No parent expects to bury his or her child.”