The 45-year-old former St Mirren and Sunderland boss departed Easter Road after a 1-0 defeat at Livingston on Wednesday night made it seven losses in Hibs' last nine cinch Premiership matches.
Hibs, who finished third under Ross last season, are seventh in the table and have a Premier Sports Cup final with Celtic at Hampden Park on Sunday week.
Ahead of the visit of Rangers on Sunday, Hearts boss Neilson said: "Obviously it is always disappointing to see a fellow manager lose his job.
"It comes as a shock to everyone whenever someone loses their job but it is part of football these days.
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"A brilliant season last season and going through a wee sticky patch and it seems to be the way now. It is the same everywhere.
"There are parts that we love, parts that we don't love but that is just the way the game is.
"I like a lot of it. I like being on the training pitch, I like the build-up to the games, I like the games. There is a lot I like.
"There are parts of the game, probably over the last 10 years that has started to become more pressurised but that is part of life isn't it?"
Neilson, however, does not believe that any potential managers will be put off by the cut-throat nature of Ross' departure and admits all managers need to have "that belief in yourself".
The former MK Dons and Dundee United boss said: "No, everyone wants to be the manager, coaches, part of football. It is the way it is.
"There's that many good coaches and managers out there just now, I am sure the list will be extremely long.
"There's a number of managers who will be keen on that job."
Hearts scrambled a late equaliser against the league leaders at Ibrox in October, when Steven Gerrard was Gers boss before he left for Aston Villa to be replaced by Giovanni van Bronckhorst.
Neilson is expecting no less of a test with the Dutchman in charge.
"Still a very good team," said the Jambos boss, whose only casualty Beni Baningime is still out with a knee injury.
"I watched them last night (in a 1-1 Europa League draw against Lyon in France) and their last few games as well.
"There are some slight changes but with any new manager coming in, unless they totally change the system, which they haven't - maybe a wee alteration in the middle and with the wide players - it probably won't be until the January window that we will see a bigger change within the squad if we are going to see a change."
Neilson revealed Liam Boyce and Michael Smith have shrugged off knocks and he hopes Baningime will be back before the Edinburgh derby against Hibs at Easter Road on January 3.
He said: "Smith and Boyce will be fine, both trained today.
"We are going to try to get Baningime back for the game before the derby but that depends if he recovers."