The Gunners dominated their FA Cup third-round replay at the Emirates Stadium but had to wait until the 86th minute before a Jack Wilshere goal gave his side a 1-0 win, and secured them a place in the next stage of the competition.
The victory was their first of 2013, and Gibbs wants more of the same in their next match.
"We have to start on the front foot," Gibbs told the club's official website. "When we do that, teams find it difficult to play against us. We have to keep that in mind.
"This can be a really lively and intimidating place, especially when everyone is up for it. We need to be doing that every week so that people know that when they come here, they're not going to get an easy game.
"Performances on nights like tonight are what we want to be doing on a regular basis."
Arsenal travel to Chelsea in the Premier League on Sunday.