Arsenal forward Theo Walcott says the Gunners have to challenge for next season's Premier League title after they successfully retained the FA Cup.
Walcott, 26, scored the first goal as Arsenal comfortably defeated Aston Villa 4-0 in the final at Wembley.
But the Gunners came third in the Premier League, 12 points behind champions Chelsea, and have not won the league title since the 2003-04 season.
"The Premier League has to be the next target for us," said Walcott.
"That's two FA Cup wins now but this is one of the best squads we have had at Arsenal so we should be achieving more. We need to start well in the Premier League next year."
Walcott suffered a serious knee injury in January 2014 that saw him miss the 2014 FA Cup final, where Arsenal beat Hull City 3-2 at Wembley.
The England international only played two games in November before another injury kept him out for a further two months.
But he finished the season strongly with a hat-trick in Arsenal's last Premier League match, a 4-1 win against West Brom as Walcott was preferred to Olivier Giroud up front.
|Glory, glory Arsenal|
|Arsenal have now won the FA Cup 12 times, more than any other team.|
Walcott opened the scoring in the 40th minute at Wembley before further goals from Alexis Sanchez, Per Mertesacker and Giroud secured the victory.
"I missed all this last year and to be part of it this year is a dream come true," added Walcott.
"My family are here and I have worked so hard, as has everyone to do this. I want to thank the manager for picking me and having faith in me and hopefully I repaid him.
"I also want to thank the physios and everyone who has looked after me. This is for them."
'My hunger is great. I want to do well'
Arsenal boss Arsene Wenger has now guided the Gunners to two trophies in two seasons after eight campaigns without winning any silverware.
"We have shown that we are a real team and can deal with pressure," said Wenger. "I congratulate the players, the staff and the fans. We are so happy.
"I had a difficult week to pick the team. But when confidence and sprit is so good it helps. I am very proud. Our club is doing well and if I can personally do well then it's even better.
"I have two more years of my contract and my hunger is great."
Wenger has won the Premier League three times, with their last success coming with the 2003-04 side that remained unbeaten throughout their league season.
He added: "Of course I think we can push on. Why not? We have won the league in the past when we have had potential to do it and that's what we want to do again.
"That's what we want to show next season but you also don't know how good the other teams will be.
"It is about consistency at the top level and in the past we have won leagues when we have been consistent."
'We really wanted this one'
Arsenal midfielder Aaron Ramsey is also adamant that his side can win the Premier League title in 2015-16.
"It's a great feeling," said Ramsey. "We really wanted this one. Winning back-to-back FA Cups is not an easy thing to do and we have done it.
"Now we can look forward to next season and kick on and give it a real go in the Premier League."
'If we keep this squad we have a good chance'
Striker Olivier Giroud scored Arsenal's fourth goal in injury-time after coming on as a substitute in the 77th minute.
He feels it is vital that the key players remain at the club.
"If we keep this squad, with one or two more players, we will have a good chance to challenge for the title," said Giroud. "The Premier League title is the target. Hopefully we will be there."
|Arsenal's win in numbers|
|12 - Arsenal moved one win ahead of Manchester United to become the club with the most FA Cup final victories.|
|6 - Arsene Wenger is the first post-war manager to win the FA Cup six times.|
|4 - The Gunners have joined Wanderers, Blackburn Rovers and Tottenham in retaining the FA Cup on multiple occasions.|
|2 - Aston Villa mustered just two shots in the entire game and both were blocked. Arsenal had 16 shots.|
|13 - This is only the 13th time that a team has scored four or more goals in an FA Cup final.|
|2 - Alexis Sanchez is only the second Chilean to score in the FA Cup final.|
|100 - Arsenal midfielder Santi Cazorla was the only player in the final to have 100 touches.|