The Gunners dropped four points in the space of six days last week, as Chelsea battled through to a frustrating goalless draw following Wigan's shock win at Emirates Stadium.
Nevertheless, Arsene Wenger's men still have their fate in their own hands - three points ahead of Newcastle, who have a match in hand and an inferior goal difference, while Tottenham's challenge for third was dealt perhaps a fatal blow after they went down 1-0 at QPR.
Arsenal travel to Stoke on Saturday and Gibbs knows if the Gunners get themselves back in the right form, it will not matter what anyone else does between now and full-time on May 13.
"We shouldn't lose focus now. We have nine points to win, and we have a position to secure for next season. We must do that," the defender told Arsenal Player.
"It has been tight all season. A lot of teams are competing and anything can happen.
"We have to finish the season strongly.
"The way we see it is that if we win our three games then we secure our position. We have three cup finals left to play."
Wenger felt Arsenal had played "with the handbrake on" and lacked the usual fluidity to their passing against Chelsea, who offered little attacking threat as they warmed up for Tuesday night's Champions League semi-final second leg in Barcelona.
Right-back Bacary Sagna accepts the Gunners must improve if they are to get a positive result at the Britannia Stadium.
He said: "Against Chelsea we struggled to pass the ball as we are used to. We weren't with the ball as much and we struggled to create chances.
"But at least we did not lose and we kept a clean sheet so we have to look forward to the next game.
"We want to qualify [for the Champions League] and we want to finish third. It won't be easy, but we want to do it.
"Everyone wants to qualify for the Champions League.
"It will be down to us, we have our destiny in our own hands."
Wenger feels Arsenal may well have to win all of their final games - which also include the visit of Norwich before a last-day trip to West Brom - to make sure of third place, which in itself would be some achievement given the Gunners' appalling opening to the Premier League campaign.
Arsenal, however, saw winger Theo Walcott limp off against Chelsea with a hamstring injury which will sideline him for the rest of the domestic season.
With Spanish playmaker Mikel Arteta also out because of an ankle problem, Wenger will be hoping midfield duo Tomas Rosicky, who played on Saturday despite a bout of sickness, and Abou Diaby, back from a string of niggling injuries, can stay fit.
The Arsenal manager said: "I hope Diaby can play an important role in midfield, but I am a bit cautious because he only played 25 minutes. In the last three games I hope he can help us.
"In fairness, Rosicky was not even supposed to play against Chelsea. He woke up sick.
"I am grateful because he wasn't well and he still played and gave everything.
"To miss Arteta and Rosicky at the moment is just too much on the creative side of our game."
Arsenal are expected to sign German striker Lukas Podolski in a £10million deal from Cologne in the summer, while speculation continues over whether captain Robin van Persie, who on Sunday night was named PFA Player of the Year, will agree a contract extension.