The Gunners head into the game having lost 4-0 to AC Milan in the Champions League, and being knocked out of the FA Cup by Sunderland.
A win against their rivals, who told a 10-point advantage over Arsenal, is vital in the push towards Champions League qualification for next season.
Gibbs is aware of how disappointed Arsenal fans have been in the past two weeks but hopes the players will be able to banish the past two weeks with a solid result against Harry Redknapp’s men.
“It’s more than just another fixture, it has something special and we can use it to put things behind us,” he told his club’s official website.
“We owe the supporters a lot – we have to hold our hands up about what’s happened in the last week or two, we know that we didn’t do what was required of us and everybody has been feeling very apologetic towards the Club and the fans.
“But this is the game in which we can overcome it, and there’s so much to lift ourselves for.
“We’re still in the top four in the Premier League and I’m sure we can stay there.
“Spurs have improved a lot, though, and you have to give them credit. Any team that’s in their position at this stage of the season has clearly done well, so we’re in for a real battle.
“All I can say is that we’ll be ready.”
The England international has seen his season disrupted by injury and he revealed how frustration can creep into a performance with so many players missing at the Emirates.
Gibbs added: “At one point we had so many players out, and it just hurt to see the team effectively cut in half.
“It was so frustrating, and when you can’t help the team you almost blame yourself in some ways. You wonder why it’s happening, and just want to get back as soon as possible.”