The defeat at St James' Park saw Newcastle drop back into the drop zone, but they were denied a goal by a controversial decision by Webb.
Newcastle were trailing 1-0 to Fulham when Viduka headed home a 50th-minute Danny Guthrie corner.
Referee Webb ruled out the strike for a foul on goalkeeper Mark Schwarzer by Kevin Nolan, although television replays suggested Shearer's side were desperately unfortunate.
Perhaps significantly, Webb was fourth official at St James' Park on Monday evening when Nolan's block on Matthew Bates allowed Steven Taylor to equalise and set his side on the road to a 3-1 derby win over Middlesbrough.
Manager Shearer and assistant Iain Dowie confronted the official as he left the pitch, and the manager was still fuming after the game.
Disappointed"We are bitterly disappointed at the disallowed goal," fumed Shearer.
"I have seen it and I can't see anything that's wrong with it.
"Probably what has happened is the goal on Monday night from Steven Taylor has been highlighted that much this week that one or two people have thought, 'We might try to clamp down on that this weekend'.
"You are allowed to put someone in front of the goalkeeper - I am not aware that you are meant to get out of the way of him.
"I thought their player was blocking him more than Kevin Nolan was, so I am disappointed with that."
Asked if he had managed to speak to Webb, Shearer said: "Not yet, but I am going to try.
"I thought he got the big decision wrong today. When he looks at it, he might think that as well."
DestinyThe Magpies find themselves back inside the bottom three and need to get a better result at Aston Villa next Sunday than Hull, who face champions Manchester United at the KC Stadium.
Shearer said: "It's out of our hands. We have got to better Hull next weekend. Whatever they do, we have got to better them.
"But it ain't over. I am sure there are going to be twists and turns next Sunday afternoon.
"But that's football, isn't it? From the highs on Monday evening and this week, we have been brought back down to earth again.
"I was always aware of 'after the Lord Mayor's Show', and we have tried to do everything to make sure that wasn't the case.
"But we were playing against a very good Fulham side who are well organised."