But after failing to convert their chances Owen Coyle's side were lucky to escape with a draw after Jermain Defoe equalised on the hour before Jussi Jaaskelainen saved a late Tom Huddlestone penalty.
"The amount of chances we created today we should probably have put them to bed," Davies told ITV1.
"We let them back into the game and Jussi made a great save to keep us in the tie.
"I think we were better in the first half but as you would expect they came out and played better in the second half."
Jaaskelainen was pleased to ensure his side would stay alive in the competition with his penalty save after Sam Ricketts had been punished for handball.
"It was a nice feeling to save the penalty," the veteran goalkeeper said. "Sometimes it goes my way, I just decided to go and saved it."
Davies believes Bolton, who lie second from bottom in the Premier League table, proved in he game that they will be more than a match for Tottenham when they resume their battle in the return leg at White Hart Lane.
"We've lost home advantage but we've proved we can outplay them at times," he said.
"The amount of chances we created we'll take a lot of confidence from that.
"We'll go down there and give it a good go, we're still in that hat, so who knows."