Kiwomya's position had become the subject of speculation after Notts lost six of their first seven League One matches.
However, Trew publicly backed the manager ahead of the club's 2-0 victory over Tranmere last weekend, which was their first win of the season.
"Ray's been very good and I just hope he keeps his faith in me like he has been doing and we can go on from there," Kiwomya told the Nottingham Post.
"Once the players see that it helps. But ultimately it comes down to myself, my staff and the players. We have to entertain the fans, we have to make sure we're committed to the cause and we have to turn it around.
"The chairman can only say so much, the fans can only take so much. It's up to us to keep going on the pitch and producing the performances like we did against Tranmere. It's really important to me to build on that, I don't want to be disappointed."
Notts face Carlisle United on Saturday.