In the first meeting between the two traditional rivals in almost three years, Leigh Griffiths opened the scoring in the 10th minute with a header before a stunning drive by Kris Commons on the half-hour sealed a place in the final against Dundee United on March 15.
The Hoops boss was delighted with the “unbelievable atmosphere” on a “very good day” but was horrified by the state of a new pitch only laid in November after Hampden had been turned back into a football venue following its use in the 2014 Commonwealth Games.
“We are a passing team and you had no chance to pass the ball on that pitch,” said Deila.
“The quality of the pitch was not how the semi-final of the Scottish League Cup should be. It makes it very hard for players. It was very hard to entertain our fans.”
Celtic skipper Scott Brown was just as scathing about the surface. He said: “That’s the worst pitch I’ve played on in a long, long time. Every time you were changing direction the pitch was coming away.
“Just look at Kenny Miller (Rangers) going down the line. He could easily have done his cruciate there.
“It’s shocking that our national stadium is like that.”
However, it was perhaps testament to how comfortably Celtic beat the Championship side — keeper Craig Gordon did not have a shot to save — that the focus was on the pitch. Deila was content with the margin of victory.
“I think 2-0 was a fair result,” he said. “In the first half we had four chances and scored two, that is okay.
“We didn’t have many chances in the second half but they did not have shot on target. I said to go for three at half-time, we didn’t manage that but we killed the game.”
Celtic, sitting top of the Scottish Premiership, take on Dundee in the Scottish Cup at Dens Park next weekend with Deila’s dream of a domestic treble still on. The Hoops also have a Europa League last-32 clash with Inter Milan to look forward to later this month.
CELTIC: Gordon, Lustig (Matthews 84), Denayer, van Dijk, Izaguirre, Brown, Biton, Commons, Johansen, Stokes (Forrest 74), Griffiths (Guidetti 68).
RANGERS: Simonsen, Foster, McGregor, McCulloch, Wallace, Black, Aird (Daly 46), Law, Hutton, Smith, Miller (Clark 81).
Referee: Craig Thomson.