The Gunners remain sixth, but moved to within four points of arch-rivals Tottenham following last night's emphatic home win, which was sealed after four goals in the space of 10 minutes at the start of the second half.
Podolski had earlier blasted in an equaliser to cancel out James Collins' fine strike before then going on the rampage down the left, setting up goals for Santi Cazorla, Theo Walcott and Olivier Giroud, who had put the hosts in front at the start of the second half.
Despite their rousing display, Podolski knows it will count for little should the Gunners not produce the same kind of display against Liverpool next Wednesday, when the Premier League campaign resumes after an FA Cup fourth-round tie at Brighton on Saturday.
"It was one game and we have three points which is important, but we have 15 games more to play. It is not about saying, 'today Arsenal are back', because we need more of these games and more of these points. Then I think we are back in the top four," the German said.
"There is enough time to get back in the top four, and a lot of points to play for.
"We need more of these games and then we are back in the first four.
"We must believe in our game and our players.
"After the two defeats against Manchester City and Chelsea, the atmosphere was not so good, but now we have won 5-1 and we look to the next game in the FA Cup."
Podolski chalked up his 11th goal last night, as his impressive integration continues following an £11million summer move from Cologne.
The 27-year-old has, though, completed only a full 90 minutes in the Premier League once, and was again substituted last night.
Podolski has been deployed to great effect down the left, rather than a preferred central attacking role, but the German just gets on with the job at hand.
"When you are a footballer, you will not always play 90 minutes. Sometimes you are not happy, but this is not important for me," he said.
"I do it well - I fight for Arsenal, for the club and team and this for me is important.
"We have a lot of great players. The coaches don't change the full-back or centre-back - you change always the positions in the front who create something.
"You have great players and it is not a problem when I am substituted."
Fellow summer signing Giroud netted his first goals in six games last night with a well-taken brace.
The France international is now also in double figures and the former Montpellier frontman is confident there is yet more to come.
"It is a good thing to reach this number [of goals], but I want to keep going and score more goals," Giroud told Arsenal Player.
"I know my team-mates very well, so I feel really good in games."
Giroud hopes Arsenal can now kick on to close down Spurs.
"It was important to win because Tottenham are on a good run. We have to concentrate on the Champions League places - it is our objective and we really want to get there," he said.
"If we play like against West Ham from the kick-off, it will be much better for us."
Arsenal head into their FA Cup tie on the south coast with a doubt over captain Thomas Vermaelen, who went off last night after twisting his ankle.
Midfielder Abou Diaby could be back in contention having been rested last night as his rehabilitation from a long-term thigh injury continues.