Celtic assistant manager John Kennedy has refuted suggestions that Rangers have now got the Hoops' number after Steven Gerrard's side came out on top at Parkhead before the winter break.
Rangers had been the better side in the Betfred Cup final between the two at Hampden Park earlier in December but Celtic retained their trophy with a narrow 1-0 win.
However, Rangers' first victory in the east end of Glasgow in over nine years took them to within two points of the Hoops at the top of the Ladbrokes Premiership with a game in hand.
Speaking from the club's winter training camp in Dubai, Kennedy told Sky Sports that Parkhead deficiencies on the day were key.
"[Rangers] were on it, in terms of the game, they played very well," he said.
"We didn't at all so it always looks like that.
"At Celtic Park, the possession was good but we couldn't do much with it in terms of we couldn't get our front players into the game well enough, we couldn't penetrate them well enough, didn't move the ball quick enough.
"Rangers were well organised, defended well, they were rigid.
"Yes, there were things we could look at and improve upon, not just against Rangers.
"In terms of our playing style and what we want to improve in the second half of the season, that's why we are out here.
"It is always good to reflect on it but the most important thing is to get back on the training pitch, that's where you get the chance to put things right."
Kennedy admitted that Celtic are working on several signing options but although he conceded that out-of-favour centre-back Jack Hendry is one who will go, he did not confirm speculation that it will be to Hearts.
The former Celtic and Scotland defender said: "I don't know about the Hearts thing. I've not been kept up to date on that.
"But I think Jack has found himself out of the squad and on the periphery so he is certainly one who will be looking to go and get some game time wherever that may be, and get his career back on track in terms of playing games which is important for any player.
"Every window we try to improve.
"We have been looking at options and there is a couple of positions that we would like to try to add a face to, to give us more competition and improve the quality of the squad.
"We have quite an inflated squad so there will be a few who will probably go the other way.
"It is getting that balance right.
"We would like to do it as quickly as possible but it needs to be right."