Rovers looked to be heading back to the top of the table as Abdulai Bell-Baggie's first career league goal gave the home side a 29th-minute lead. But County fought back and Neal Bishop headed in a second-half equaliser that gives Kiwomya hope that there is more to come from his side.
"We are sat in the changing room disappointed," Kiwomya said. "They are a good team, but I thought we deserved to win. We asked all the questions and I thought we were the better team especially in the second half. Maybe we just didn't have that rub of the green that you need at times.
"Coming here is hard, at half-time they were top of the league, so it's a point that we'll have to take. I put a little bit more pressure on myself to do even better since taking over last Friday. I enjoy it. There a lot of good players in that changing room, but sometimes you need that killer instinct.
"I think we're down to 12 games now so the games that are coming up are vitally important. But we can do it. We've got good enough players. I'm confident we can have a late charge, we've still got a good chance."
The home side started the brighter and deservedly went ahead when Bell-Baggie ran onto Michael O'Halloran's pass to slot home. But the Magpies - who saw a Julian Kelly shot saved by Owain Fon Williams in the first half - equalised after 74 minutes when Bishop rose highest to head in Alan Judge's free-kick.
Driven on by the goal, County substitute Jeff Hughes almost grabbed a winner shortly after but his shot from the right of the box bounced back of the left post.
"We fought and scrapped," said Tranmere manager Ronnie Moore. "They are a good side, there's no doubt about that. The two wingers are lively, but they don't really like defending do they? And that's really where we didn't really keep the ball on the counter-attack.
"For the goal we've got, we've kept the ball, played a great pass and Abs has gone in and scored. We just needed to push on from there. I just thought we got a little bit nervous and anxious. It was a stupid free-kick to concede for their goal."