The Premiership leaders hit the frame of the goal three times on Sunday as they looked for a third goal to finish off an Inverness team who were inspired by goalkeeper Owain Fon Williams.
But Alex Fisher headed an injury-time equaliser to seal a 2-2 draw and end Celtic’s 100 per cent record in the league.
Celtic have not kept a clean sheet in the league under Brendan Rodgers and have only had two shutouts in 13 matches in all competitions, against Lincoln Red Imps and Motherwell.
Davies admits they should not necessarily have to score two or three goals to win a game. “We have scored a lot of goals,” he said. “Fon Williams had a really good game and you can’t always score all your chances. Of course you want to be clinical but we scored two goals.
“We want to be a team that wins by one goal, and of course we can do that. If we are not quite finishing the chances and the goalkeeper is having a special day, then we are resilient at the other end and we make sure we win the game by one goal.
“The goal was second phase from a corner, you have to make sure your organisation is good from the initial corner and the second phase and we have to make sure that doesn’t happen.”
Celtic rested Kolo Toure on Sunday from a back four that has undergone major change throughout Rodgers’ short spell in charge so far. Ten players have started in defence and young players such as Anthony Ralston have been involved off the bench.
An 11th, Jozo Simunovic, could start in tomorrow’s Betfred Cup quarter-final against Alloa after returning from a knee problem off the bench against Caley Thistle.
With a full complement of defenders now available and with the arrival of right-back Cristian Gamboa, Rodgers now has the chance to mould his preferred back four.
“Continuity generally helps defence,” Davies said. “Everybody wants that settled back four but sometimes with injuries and bits and bobs, it’s not always possible. But we’ll be looking in the next few weeks if we are dominating games and can’t quite finish our chances that we give nothing away at the other end.
“We’ve got Jozo back, who came on and looked excellent, he was strong and with his passing.”
The Croatian came close to leaving Celtic on deadline day but a move to Torino fell through as he waited in Italy.
“He has responded very well,” Davies said. “He trains fantastically, he has got a great attitude and application. He is a lovely guy as well, he’s got personality. And when he goes on the pitch he wants to defend and be aggressive. And he can pass. He’s the type of defender we want and hopefully now he can go from strength to strength.”
Meanwhile, Davies rejected claims that Erik Sviatchenko should have been sent off in Inverness. Ross Draper went down in a tangle with the Danish defender as he bore down on goal.
“I’ve seen it on the camera we have got, which didn’t have replays and close-ups, and then I’ve seen an image of it,” Davies said. “Obviously it wasn’t a penalty.
“And I think that guy hasn’t had enough speed to get away from him, so I don’t think it was a foul. I think the player is waiting for the contact, he is trying to be cute on it, and I think the referee [Don Robertson] had a very good game.”