The Liverpool coach also believes that the side don't need any motivation for games such as this.
The two sides come up against each other at the Emirates on Monday evening in an early season clash between two teams who are likely to be vying for a Champions League spot come the end of the campaign, if not more.
And McAllister says they must play on that West Ham win to put the seeds of doubt into the home crowd and make Arsenal unsure of themselves.
“We’ve got to try make Arsenal a little bit unsure and not as confident as they can be,” he told liverpoolfc.com.
“It’s important to be really competitive against them. If we make a bright start, there might be some doubt within the crowd. They’ve witnessed a home defeat already and you’ve got to try and put those seeds [of doubt] in there.”
No need for motivation in these fixtures
The former midfielder is also expecting the game to be another classic between the two sides, with the fixture having served up a number of fascinating clashes over the years.
Last season the Reds were heavily beaten when they visited the Emirates, with a fine display from Arsene Wenger’s side having saw them dismantle their opponents with ease.
Far from being nervous though, McAllister insists that this is the type of game all players want play in, saying there is not motivation needed for the squad.
“These are the games that everyone within the dressing room wants to play in,” he added.
“They take care of themselves and there’s not a lot of motivation required. Both sides like to try and play attractive football. There is no inch given and we’ve got to go there and make sure we realise we’re going to be in a game – and I am sure that will be the case.”