The Soldiers started the match brightly, creating chances that put the defending champions under pressure, but lack of composure in front of the posts was their main undoing.
Nyaudo has promised to 'work' on their weaknesses going into the next round even as time slowly ticks down.
"I blame my strikers for this outcome, they had many chances to score but they did not take them.
"The pressure, as a result, turned to my defense and we ended up losing the match.
"We will have to go and work on it and ensure the same mistakes do not happen."
Ulinzi are currently seventh on the log with 30 points; 13 adrift of leaders Gor Mahia.