Saturday's 3-2 win over Tottenham, having squandered a two-goal lead, was only their second Barclays Premier League victory since November 29.
It kept the side four points clear of the relegation zone and Taylor hopes it will provide a catalyst to a run of better results and ease the pressure on Megson, who was abused by fans in last week's 2-2 draw at Blackburn.
“Fans pay their money to have an opinion and I understand that,” said Taylor. “But when they are saying things that have a detrimental effect on the team then I don't agree with it.
“Maybe we have got - and I'm talking about a small minority here - some fans who have never liked the manager but at the end of the day, results speak a lot louder than everything else.”
Taylor said confidence within the squad was boosted by a recent warm-weather training camp in Dubai and a return to winning ways.
The midfielder said it had been important to beat Spurs having let slip a 2-0 lead against local rivals Rovers.
“We make such hard work of things. We are a lot better than we think we are,” he said. “We need to start believing in ourselves and if we do, we'll start picking up more points.
“It's a different place after a win. It invigorates everyone and puts smiles back on faces.
“There are 15 games left and I'm sure we can build on this against Everton away (on Saturday). That's a massive game for us again.”
Taylor revealed he was one of seven senior players called to a meeting with Megson on Friday to discuss the Blackburn performance and also club captain Kevin Nolan's departure to Newcastle.
“We had a good chat. It made me laugh last week reading in the paper that the club was in crisis and that there's a dressing room rift.
“There's not one person in there who you would describe as a bad egg. We are all pulling in the same direction.”
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