The French midfielder re-signed in August, having previously spent four years with the Club between 2004 and 2008.
Walcott is impressed with the way his team-mates have stuck together in recent months and believes an upturn in communication goes hand in hand with Arsenal's fine form.
"I think everyone is talking and everyone is communicating and that's helped," he said.
"The likes of Mathieu coming in, he's a leader and you saw him bossing people around, that's what we need.
"It showed from last season how we wanted to be in the Champions League and I think we are pushing on now.
"When you go to one of the toughest places in Europe and win [at Bayern Munich] you've got to think you are a very good team.
"At times I think we didn't believe in ourselves and I think it showed that towards the end of the season we knew we wanted to be in the Champions League, we want more games like that and that's why everyone's working hard for each other and we will continue to do that on a high level.
"We haven't got the biggest squad in the world and we've got a lot of injuries which doesn't help but the players that are playing are contributing bodes well.
"It's important that we stay focused and stay fit which is very crucial as well because we don't want to lose any more players, but as soon as the players come back there's going to be competition for places. That should be a good thing for Arsenal and I think we will definitely challenge this year."
The form of Aaron Ramsey has helped Arsène Wenger's team to six consecutive wins. Walcott says he is "honoured" to play alongside the Welsh midfielder and is glad to see him excelling.
"He had one of the worst injuries in football and he's had a hard pre-season," Walcott said. "He's worked very hard and it's definitely paying off now. He's enjoying his football and he's difficult to get off the pitch.
"He loves getting on the ball and he's added something different to his game now with his goals. People used to criticise that part of his game but I see him in training every day, he's a totally different player and he's like a new signing. It's an absolute honour to play with him at the moment.
"I think you can see there's a lot of players are having fantastic starts to the season like Aaron Ramsey who has been incredible to play with. It just shows because everyone believes in each other and the trust is there and that's all we need."