Even though Champions League qualification now looks virtually assured, Gilberto is not about to let his side relax.
The stand-in captain believes Arsenal eased off after taking the lead against Manchester City on Tuesday night and has warned that they cannot do the same at Tottenham on Saturday.
"I played there when we won the League in 2004," he said. "Although many of the players have now left, the traditions of the match are still the same.
"We will need to keep our minds strong because this is the kind of game where you do not have time to relax for one minute.
"We know that in the matches against Tottenham, if we do not play at 100 per cent then it will be difficult.
"It is important to keep our concentration high over all of the final four games.
"Against Man City, it looked a bit strange; after our first goal we relaxed a little bit. Sometimes we can play very nice football and draw or lose. Against City, we did not play our best, but got three points."
Arsène Wenger's side have now recorded welcome victories in their last two games. They are currently third and seemingly secure in the Champions League places. There will be no silverware this year but Gilberto expects the side to develop next term.
"We have been in transition and it has been so hard for us," he said. "There have been some bad times this year.
"But I really believe that for next season the young players in the squad will have grown in confidence and experience. They will be stronger than we have been in the last two years."
Copyright 2015 The Arsenal Football Club plc. Permission to use quotations from this article is granted subject to appropriate credit being given to www.arsenal.com as the source 18 Apr 2007