Deila is under pressure following disappointing European and Scottish League Cup campaigns, while Aberdeen are chasing Celtic hard at the top of the Ladbrokes Premiership.
Warburton and his team could put more pressure on the Norwegian in the William Hill Scottish Cup semi-finals, but the Rangers boss feels his counterpart is on the end of some ill-merited criticism.
Warburton told talkSPORT: “I referred to the goldfish bowl and it is a really passionate football city. I thought London was a football city and then you come to Glasgow and really they live and die for their football.
“There’s 14-15 pages every day in the papers, there are radio shows every evening, and it’s scrutiny beyond belief. The fans phone in and it fuels the fire.
“So, he’s top of the league. They had a difficult European campaign, okay, but what more can he do?
“I do feel some sympathy for him but I think you know when you join a club like Celtic or Rangers, you know what you are putting yourself up for, that’s for sure.”
Warburton, whose Championship leaders face Celtic in mid-April, added: “We took 9,000 officially to Kilmarnock on a Tuesday night, pouring with rain, on a Champions League night, but there were nearer 11,000 unofficially. It’s an unbelievable support.
“This is the size of the club and we have got to enjoy it. The players have a responsibility, we have a responsibility and if we can get the environment right where they enjoy the responsibility, we will be in a good place. You have to thrive on it.”
Warburton attempted to focus his players on their league game against Morton on Friday night immediately after Sunday’s draw, but he is well aware of the importance of the derby.
“I was at Belfast Airport, I had been to see a player,” the former Brentford boss said. “I heard the draw and turned my phone off to get on a 30-minute flight and I had 27 missed calls by the time I landed. That gives you a clue as to what it is.
“It’s a fantastic draw and it is a challenge to test ourselves. It’s a game at the national stadium and there will be a 50,000 sell-out and we look forward to it
“There is no doubt we will go into the game well-prepared and ready for the challenge but between now and then we have some very important league games and the week before we have the Petrofac Cup final.”
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