The Blues visit White Hart Lane on Saturday on the back of a 4-0 thumping of Leeds United, while we are seeking a first home win since beating the same team back in August.
Everton have had a mixed start to their Premiership campaign, with three defeats, two draws and two wins. Similar to ourselves, their season has sprung to life in the last week - in Everton's case with Carling Cup victory over Stockport and the win over Leeds.
"They are looking a good side and ticking along quite nicely now," reasoned Anthony. "It will be a tough game, but we need to come out and put on a good performance and get a convincing win.
"I feel we can do it, it will be about stamping our authority on the game.
"We've let in a lot of goals in our last two home games and we need to put that right. For the fans, players and management - we owe a good performance to show how we can play."
Everton boss David Moyes is blessed with a number of striking options at the moment, with Tomasz Radzinski and Wayne Rooney supplemented by the on-loan ex-Blue Francis Jeffers and the returning Duncan Ferguson.
The latter has found the net four times since coming back from injury and could hardly be described as a player that defenders look forward to playing against.
"All the strikers are very different and have different attributes," added Anthony. "Whichever one you play against you will be in for a tough game but, on the day, I will just have to apapt to whoever I'm playing against.
"I played against Ferguson a couple of years ago in one of my first games. He is strong, agressive and very good in the air - probably one of the best. He is a tough one to play against, but you have to rise to the challenge."
And what about young Rooney?
"Very good with an unbeliveable future."
Anthony Gardner says the team must quickly stamp authority on the game against Everton in order to reverse recent home form.