The stand-in captain, who scored 76 not out as Yorkshire replied to 177-4 with the same score, said: “It was my fault in the chase. I should have knocked them off.
“We’ve got a point, but it’s not good enough given the position we were in.
“I was the one who batted through (the innings), and it should be on me to win the game for the team; I didn’t.
“If it was someone else in the same position, it would have been on them; when you bat through the innings, you should control it and win the game.”
Yorkshire blew a great opportunity to gain their second victory in the competition going into Friday’s Roses clash against leaders Lancashire at Old Trafford.
Instead, they are sixth in the table with a record of one win, three defeats, two no-results and a tie, with five points from seven fixtures.
“It was definitely a point lost,” added Kohler-Cadmore. “Throughout the chase we were in front.
“They bowled a couple of good overs towards the end, but even then I should have seen it home for the team. I felt like we deserved to win, but we’ve lost a point.”
Jim Troughton, the Birmingham Bears’ head coach, admitted that his side got out of jail.
“With six overs to go, we looked dead and buried,” he said. “It looked like a game only Yorkshire could lose.
“But we managed to keep our composure in the field, and that paid off.
“Fidel (Edwards) didn’t quite get it right today, but he’s been fantastic for us previously and he still had the bottle to take the ball in the last over and stop them getting past us.”
Troughton, whose team are fourth in the table with a game in hand on the top three of Lancashire, Worcestershire and Nottinghamshire, felt that the dramatic finish put last month’s World Cup final into perspective.
On that occasion, there were two ties between England and New Zealand (the match itself and the Super Over), before the hosts won on boundary countback.
“I said to Dom Bess (the Yorkshire off-spinner) on the boundary towards the end, ‘Imagine if this was the World Cup final!’” said Troughton.
“You can’t even begin to think what they were going through with that.
“Thankfully, our players managed to hold their nerve and we’re still in a good position in the league.
“We have a game in hand, and Leicestershire have just beaten Worcestershire to help even things up a bit at the top.”
Yorkshire play their return T20 fixture at Birmingham on Friday, August 30, their final match of the group stage.
The teams also meet in the last game of the County Championship season at Edgbaston from September 23.