The visitors also saw a score by wing Harry Robinson ruled out in controversial fashion that would have drawn the sides level with 13 minutes left.
Leinster eventually secured the bonus point win with two scores in the final quarter.
But Davies was pleased with reaction of his Blues, after defeat to Zebre last time out, and looked ahead to the clash with Edinburgh next Sunday at Cardiff Arms Park.
"I wanted us to play with pride and emotion against Leinster and we did that," he said.
"For long periods of the game, and certainly up to 67 minutes, we were very much in it and we were unfortunate not to get the try for Harry Robinson when it was adjudged forward when it came off their hooker.
"There are still things that we need to work on, but what we are trying to achieve is there and we have got to be tidier doing it.
Looking ahead to the Edinburgh game he added: "They are all big games in this league and we want to win every game we play, especially when we play at home.
"Last week was particularly disappointing, but this has restored the pride in the group.
"Next week we have got to make sure we get there. We need a massive performance and we need a result for us and the supporters too.
"We got stuck in tonight, the hits were big and we carried the ball hard. The forwards were magnificent.
"We had a turnover in the corner with seven men at scrum time and we just failed to clear it and they get over the next time.
"There was lots of fight and fire tonight which was pleasing. If a couple of passes start going to hand and decisions go our way then we will get there.
"That is part of growing up I suppose, but we are growing together and tonight we showed at the home of the champions that we have got some steel about us."