Both decisions took a long time to reach, despite the directive that the system should only be used to over-rule "clear and obvious" errors.
Three incidents were checked on Monday as Danny Ings waited to see if his goal would stand, which it eventually didn't, after three and a half minutes of deliberation.
The goal was eventually chalked off as Edison Cavani was adjudged to have been fouled in the build-up to the goal.
"We should not be using VAR in this game if we can't use VAR in every FA Cup game, wherever that may be. You shouldn't be using VAR in this game," said former Newcastle United striker Shearer.
"Is it a clear and obvious error? I don't think it is because Cavani isn't going to get near the ball."
Former Aston Villa and Man City defender Richards agreed with Shearer's view on the use of VAR in the competition.
"I don't know if Cavani is going to get there and it took so long to make a decision it is ridiculous," he said.
"How can they have it in one game and not other others? The inconsistency is ridiculous. It is not acceptable to take that long either as the fans have no idea what is going on."
Manchester United's win set up a fourth-round tie with Middlesbrough.
It was the second day running a televised FA Cup tie was effectively decided by a controversial VAR decision after Leeds's 2-0 defeat to West Ham.
The Hammers' decisive opening goal, which arrived via Manuel Lanzini in the 34th minute, was sent to VAR to check if the goal should be ruled out for offside.
Referee Stuart Attwell and his assistants allowed the goal to stand but Leeds' players, led by Luke Ayling, argued that West Ham forward Jarrod Bowen - who latched onto the ball and ran across Illan Meslier after Michail Antonio crossed into the area as Nikola Vlasic and Leo Hjeld challenged for the ball - was offside and impacting the play.
Lanzini eventually finished but replays showed Bowen was beyond the last defender when Vlasic initially touched the ball, therefore impacting Meslier's ability to make a save.
Despite many expecting the goal to be ruled out, a lengthy VAR review by Peter Bankes and his assistant Lee Betts allowed the goal to stand.
Leeds captain Liam Cooper tweeted that the decision was a "shambles" while club owner Andrea Radrizzani also suggested on social media that Bowen was clearly offside.
The YEP have reported that the goal was allowed to stand as both the VAR and AVAR felt that Bowen did not impact the ability of Meslier to attempt to make a save.
The phase of play was then re-set when the ball came off Vlasic again with and Bowen behind the ball it put him in an onside position.
The law on offside set out by the International Football Association Board, states: "A player in an offside position at the moment the ball is played or touched by a team-mate is only penalised on becoming involved in active play by interfering by playing or touching a ball passed or touched by a team-mate or interfering with an opponent by preventing them from playing or being able to play the ball by clearly obstructing the opponent’s line of vision or challenging an opponent for the ball or clearly attempting to play a ball which is close when this action impacts on an opponent or making an obvious action which clearly impacts on the ability of an opponent to play the ball."
Despite the frustrating nature of the decision for Leeds, Whites boss Marcelo Bielsa refused to complain about the officiating or the result as his side exited the FA Cup.