The Norwegian boss came under fire after the Hoops’ ignominious exit from the Europa League where they finished bottom of their section.
Deila came in for more criticism following the 2-1 defeat by Motherwell at Parkhead last weekend, although Celtic remain one point above Aberdeen at the top of the Ladbrokes Premiership table with a game in hand over the Dons and with the domestic treble still a realistic prospect.
“It is life as a manager and especially at the Old Firm,” said Neilson, speaking ahead of Sunday’s clash with the Hoops at Tynecastle.
“There is always that constant pressure and I think Ronny has handled himself well.
“It is part and parcel of the job at big clubs like Celtic that there is always someone trying to put pressure on you.
“Celtic is a team that is used to playing under pressure, a team that is used to having to get results and Sunday is no different.
“They will come with the same mentality as they always do, not matter if they have been beat the week before or they have not been beat.”
Neilson is looking forward to what is traditionally a feisty fixture between two of Scotland’s biggest clubs.
He said: “Aberdeen, ourselves and Celtic are three teams that pull the biggest crowds (in the top flight) so it is a big game and one that players want to be involved in.
“It is sold-out again which is great.
“It is important that the two teams put on a show, the first 20 minutes will be quite intense and hopefully we will start playing a bit of football after that.”
Despite not winning any of their last four matches - three of which have been drawn - the former Hearts defender is relaxed about the prospect of facing the champions.
“We haven’t picked up the points we would have liked recently but the performances have been good,” he said.
“The players are in good condition and starting to play a bit more football than they have been recently and we would like to carry that into Sunday.”
Neilson, however, will have to do without striker Juanma Delgado, who was handed a two-match ban for being sent off in the goalless draw against St Johnstone last week for a headbutt on David Wotherspoon.
The Gorgie boss said: “He is one of our key players and it is always makes it difficult when you lose one of your main strikers.
“He is a player that we try to communicate with a lot and he is just disappointed with his reaction to the incident last Saturday.
“We had a chat about how he needs to try to manage that.
“I hope so (got message). He is an intelligent boy who let himself down a wee bit.”
• Be sure to like the new Scotsman Sport page on Facebook