The Celtic boss has been backed by his rival at Rangers following Sunday's Old Firm defeat.
The Rangers boss defeated his opposite number in Sunday's Scottish Cup semi-final courtesy of a penalty shoot-out, which will signal his exit at the end of the campaign according to Sky Sports.
But Warburton, who met Deila for the first time in person last week, took little pleasure in increasing pressure on the Norwegian.
Asked if he had sympathy for the Bhoys boss, Warburton told Talksport's Drive show: "Yeah, absolutely. The media up here is very intense.
"We had a press day today and I made that comment that Ronny - I met him for the first time at the pre-game conference, really nice guy, good football person - he’s received some brutal... you know... up here, so to speak.
"It’s been really harsh in the press. I don’t think people deserve that. Managers expose themselves, you have good times, you have bad times - I understand that.
"But he’s a good guy, he’s doing his best, they’re going to go win the league and I said to the press today: what represents success for clubs? If the target is go and win the league, he’s done that. If they said to him you have to get into the group stages of the Champions League that may be a different target, a different proposition."
Deila arrived at Celtic two summers ago from Stromsgodset and is on a rolling 12-month contract in Glasgow.
The 40-year-old lifted a Premiership and League Cup double last season and is on the verge of securing the Bhoys' fifth straight title.
But with Warburton's Rangers tipped to make an immediate challenge next season, Celtic are under pressure to produce a flawless campaign.
The nature of Deila's contract should allow for a hassle-free parting of ways.
Former Celtic defender David Moyes and Deila's predecessor Neil Lennon are the current favourites to replace him.