Wanderers recently surrendered a vital two goal lead at Blackburn in the dying minutes at Ewood Park to draw 2-2.
Megson's men were booed off by the away supporters after a result which left them precariously close to the drop zone.
Bolton appeared to have put that performance behind them when they raced into a two goal lead against fellow strugglers Tottenham at home on Saturday.
The Trotters suffered a severe case of Déjà vu when they gave away a two goal lead for the second game in succession, but this time striker Kevin Davies fired a late winner just as some home fans were sharpening their knifes.
The former Portsmouth ace is confident that his manager can prove the small section of doubters wrong.
"Fans pay their money to have an opinion and I understand that," Taylor said.
Minority"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.
"We make such hard work of things. We are a lot better than we think we are. 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. That's a massive game for us again."
The 27-year-old also rubbished rumours speculating that there had been a dressing room bust-up after the Blackburn game.
"We had a good chat. It made me laugh last week reading in the paper that the cub was in crisis and that there's a dressing room rift," he added.
"There's not one person in there who you would describe as a bad egg. We are all pulling in the same direction."