A late Moussa Dembele goal against their Old Firm rivals sent the Hoops through to the Betfred Cup final against Aberdeen in November.
Despite the narrow scoreline, the Parkhead boss claimed the performance was as dominant as the one he witnessed in 5-1 Ladbrokes Premiership win over Mark Warburton’s men at Celtic Park last month.
Rangers keeper Matt Gilks made a series of saves including stopping a Scott Sinclair free-kick with the aid of the crossbar while Erik Sviatchenko had the ball in the net, only for referee Craig Thomson to blow for foul on Gers defender Clint Hill.
“Yes, I think it was just the goals,” said Rodgers when asked if the performance had been the same as that at Parkhead.
“I think it was pretty clear. We had that same performance but we just didn’t finish the opportunities.
“Some of that was through the goalkeeper, (he) got a touch onto the bar and it came back to him.
“I need to see the header again but it looked very harsh, the one that was disallowed. When the ball comes into the box both sets of players are physically trying to command that edge to get a touch on it.
“We had other chances that could have gone in but didn’t but again it shows the mentality in the team, they kept going, didn’t get disappointed, had great discipline and eventually got their reward which they deserved.”
Rodgers admitted some relief at getting the winner in the nervy closing stages.
He said: “Yes, because I thought we were very dominant today in terms of chances and power and strength and quality in our game.
“Sometimes you never know, if the chances don’t go in and you don’t get that little bit of luck you are always vulnerable to a counter attack.
“Tactically the players were brilliant, we stopped them building.
“Then when we had the ball, we created opportunities and looked a real threat going forward so every element of our game was at a high level.”
Rangers were understandably more cautious given their last meeting with the Scottish champions which, along with Celtic’s control of the match, restricted their attacking forays.
Mark Warburton tried to spice up his gameplan by throwing right-back James Tavernier into a more advanced role with the more defensively minded Lee Hodson keeping things tight at the back. While it worked for a long spell, Celtic’s sustained pressure eventually told. However, Warburton considered the game as evidence that his side are not so far behind Celtic.
He said: “We’ve worked very hard to move forward and gel as a team and I hope you saw that today.
“They scored one goal and we didn’t — that’s the difference. They took one chance right at the death there.
“It was that type of game where one chance would change it. It was nip and tuck with chances at both ends and that one went in. It was as simple as that.
“The so-called gap is a lot narrower than people think and we have to learn from today’s performance.
“We spoke to you guys after Parkhead and said the only solution is to work hard and we’ve done that.
“It was tight right to the death there until the 87th minute. We’re getting there and the players are understanding what we want and I’m delighted with the progress we’ve made. I think the players have shown their quality. There was no lack of desire, no lack of work ethic or focus.
“There is a lot of pressure on them but we are getting there. The aim is to work hard and continue that progress.”
Gilks, Hodson, Kiernan, Hill. Wallace, Windass (Garner 70), Halliday, Holt, Tavernier, Miller (Waghorn 70), McKay (Dodoo 78)
Gordon, Lustig, Simunovic, Sviatchenko, Tierney, Brown, Bitton (Armstrong 63), Forrest (Gamboa 90+1), Rogic (Griffiths 70), Sinclair, Dembele