United parted company with their 1999 treble hero in the wake of their 4-1 defeat at Watford and have put Michael Carrick in temporary charge while the club look to appoint an interim manager to the end of the season.
The decision follows a torrid run of results for United under Solskjaer, the club great who replaced Jose Mourinho in December 2018.
He rode out a chastening 5-0 home loss to Liverpool and appeared to be back in calmer waters after a 3-0 win at Tottenham, but a comprehensive derby loss to Manchester City meant that the Watford game was essentially a must-win.
Neville told Sky Sports: "Ole will reflect with sadness but he can be proud of the work he did in the first two years. He rebuilt the soul of the club, the club was in a dark place at the end of the Jose Mourinho era.
"Ole can't complain, he's been given three years, he's been backed in the transfer market. David Moyes was given eight months and kicked out, so I don't think Ole can complain about the time he's been given and the money he's been afforded."
The former United full-back believes Solskjaer's departure had become inevitable.
"It's been coming for the past few weeks, performance terrible and results shocking. It was wimpish at Watford," Neville added.
"You're always hoping the players would respond, that the two-week international break would bring some freshness but it looked like they had the world on their shoulders, their performance levels over the last few weeks have dipped.
"When a manager can't get a performance out of his players and results are getting as bad as they are, in this game, you're going to lose your job.
"The worst thing is the performances, the team have looked all over the place. The defending is absolutely woeful, the goalkeeper and defenders and that's a back four, five that have played together a number of times.
"Watford aren't the best team in the league by a long stretch but they got mauled, Manchester United.
"What's happened this last two months I can't explain. Villarreal at home, Everton, Villa is where it started, they looked so open, so blase, they thought they could go and beat anybody.
"They've not been able to get right since. They've looked rudderless on and off the pitch and it's caught everyone by surprise.
"A couple of weeks ago I thought getting to the end of the season was the right thing to do if they could, they obviously haven't been able to do that."
Neville does not believe there is an obvious candidate available to replace Solskjaer and is not surprised the club are looking for an interim manager. He also feels the club might hope Paris St Germain manager Pochettino comes onto the market. The Argentine previously coaches Tottenham Hotspur, where his final match in charge came against Sheffield United.
"They are waiting on Mauricio Pochettino not being successful at another club. If he was to win the Champions League, then PSG wouldn't let him go," Neville added.