Arsenal lost only one league game in six against Manchester United, Liverpool and Chelsea this season, but saw their chances of winning the Premier League unravel following unexpected defeats against Stoke, Fulham, Hull, Aston Villa and Manchester City.
"We have to learn from our experiences this year, do the dirty work and get the results," said Walcott. "Like the boss said, Man United only won one game out of their matches against the top four, so it just shows how important every game is in the Premier League.
"The so-called littler clubs, away and at home, they are the points you have to make up. We have to do the dirty work, like we have learned from this year, and take that into next season."
Arsenal's Premier League campaign ended well, with just one defeat against Chelsea in the final 23 matches of the season.
"We have ended the season on a high," said Walcott.
"We have got to take that into next season now, bounce back and put in a good performance.
"We are scoring goals from all sorts of positions, the team is playing very well and are keeping the ball without conceding many goals.
"Now the boss will be telling the players to reflect on the
season, then go and have a good holiday, relax, before looking forward to next season."