Caretaker manager Kenny McDowall was critical of Rangers' first-half display as Celtic coasted to a 2-0 win in the League Cup semi-final at Hampden.
Leigh Griffiths and Kris Commons were on target as Celtic dominated play before the interval.
"I was disappointed with the manner in which we gave the two goals away," McDowall told BBC Scotland.
"The second half was much better. It's unfortunate we couldn't get ourselves a goal to make it interesting."
Rangers were more aggressive after the break and stemmed the flow of Celtic attacks but at no stage threatened opposition goalkeeper Craig Gordon.
"We had a lot of play around their goal, we just couldn't turn it into a goal opportunity," added McDowall on his team's second-half efforts.
"But when you give goals away and you don't score, you can't complain."
Rangers, second in the Championship, initially adopted a 4-5-1 formation, with Kenny Miller isolated as the lone striker.
Despite packing men behind the ball, Rangers were guilty of giving Celtic too much room in which to manoeuvre.
Stefan Johansen was completely unmarked from a throw-in as he drove in the cross for Griffiths to head in the opener on 10 minutes.
Commons then sent a powerful shot beyond Steve Simonsen, despite the keeper getting a hand to it, while Celtic spurned a few more opportunities to add to their lead.
"You set up to keep it tight and when you lose a goal like that it unsettles everyone," said McDowall, who is working his notice on a 12-month rolling contract.
Having stepped up to succeed Ally McCoist in December, the 51-year-old former St Mirren striker announced his intention to step down four weeks later.
Asked if he would be sticking around to see his contract out or joining McCoist on gardening leave, he replied: "I don't think that's a question for me, that's one for the board.
"For me this was an opportunity to get to a cup final. That's gone now, so we carry on and look forward to the league campaign."