Arsene Wenger's Arsenal sit just a point outside of the UEFA Champions League qualification places in fifth position after recovering from a slow start to the 2014-15 Premier League season.
Arsenal have only lost one of seven league matches following their 2-0 win at second-placed Manchester City a fortnight ago.
The London outfit also remain in contention for the FA Cup (fifth round) and the Champions League (round of 16).
And Gibbs, who is enjoying his best season so far, is refusing to give up hope of lifting silverware in 2015, even in the Premier League despite being 13 points behind Chelsea.
"If you look at last year, we were top of the league for the majority of the season but towards the end was where we faded," Gibbs told The Mirror ahead of Sunday's hosting of Aston Villa.
"Now we have got a chance to hit form and we'll see where we end up.
"I just look at the next game, against Aston Villa. You can't set yourself any limits. We have still got loads to play for.
"It's all there in front of everyone to see what there is to play for. We want to embrace it and take control of it."
Gibbs added: “I think Manchester City was quite a turning point, sometimes it takes a game to change the dynamics.
"Not just in the team but also in the league. It was like an awareness that we have a big say in the league.
"I think we already knew that but sometimes one game can just change that mentality."
