Sunday's 2-1 defeat to Manchester United in the league removed any hope they could come back into the title race, and many have suggested that Arsenal have faltered due to a lack of strength in depth compared to their rivals.
But club captain Gallas believes that it is simply bad luck that has counted against them this year.
"The luck went from us a few months ago. People have to understand that. We drew too many games at home, and away we lost important points."
Many felt the team would face a fight to make the top four after Thierry Henry's departure to Barcelona, but the team has shown substantial improvement on last year and Gallas is hopeful they can take it a step further in the next campaign.
"What is very positive from last season is we should finish third in the Premier League, we went to the quarter-final of the Champions League, so we have improved.
"However, we cannot accept just that because when the season started we wanted to win everything but then slowly, slowly we started to lose.
"Now at the end, we do not get anything. That is a great shame for the club. We have to speak together and to know what was wrong.
"We are not far away, but we will have to see what we can do next season.
"I hope we can get something. I am a competitor and want to win everything. You remember only the people who win trophies.
"For the fans and the club, it is important to get some cups. Now we just have to be professional and finish the season well."