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 mark 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 the players
It was very hard to entertain our fans.
"If you are going to develop Scottish football you need pitches to play football on.
"If you go four, five months with poor pitches all over the country every game is going to be in the air and that is not international football, and this is the national team's stadium.
"It has to be much better.
"Skill needs good pitches so this if not good enough."
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.
"Until that happens people don't ask questions but it's shocking that our national stadium is like that."
However, it was perhaps testament to how comfortably Celtic beat the Championship side - Parkhead keeper Craig Gordon did not have a shot to save - that the focus was on the pitch.
Deila was happy enough 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 in another way.
"We were solid in the back and kept them away from the goal."
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
The former Stromsgodset boss said: "We haven't won any trophies yet and the final against Dundee United is going to be tough.
"But everything is possible now.
"Dundee on Saturday is very important and it is very motivating to see that we can win everything.
"January was an important month for us to get everyone injury free.
"I have a good feeling about this month."
Rangers caretaker boss Kenny McDowall, who has signalled his intent to leave the club at the end of the season, cut a forlorn figure in the Hampden media room.
He added to the pitch debate by saying: "It wasn't very good but that is not an excuse."
When asked about his side's failure to get a solitary shot on goal, he said: "I think we had a fair bit of play around their goal but we couldn't get an effort on the goal.
"You need to get something on target if you want to score.
"I was disappointed with goals we gave away
We set up to keep it tight early on in the game so to lose a goal in the manner we did threw a spanner in the works which made the first half sticky.
"I thought we did far better in the second half, we just couldn't get the goal to make it interesting."
Asked how far he thought Rangers were away from Celtic, he added: "You can decide that
It was 2-0 but I thought we competed well."
Source : PA
Source: PA