Frank Lampard says Everton paid the price for "giving everything" to secure their Premier League survival earlier this week in the final-day defeat at Arsenal and assured supporters work begins now to improve the squad for the future.

The Blues headed to Emirates Stadium less than 72 hours after sealing a stunning 3-2 comeback win over Crystal Palace at Goodison Park to secure the Club's top-flight status for a 69th consecutive year.

Boss Lampard cited injuries and players needing a breather as he made six changes to his starting line-up against the Gunners, who needed to win to keep alive their hopes of qualifying for next season's Champions League.

And, despite a quick-fire Arsenal double either side of the half-hour mark, the Toffees went into the interval very much in the contest but trailing 2-1, after Donny van de Beek stepped off the bench to provide hope for the Toffees.

It wasn't to be, though, as the hosts added three more goals in the second period to consign Everton to a 5-1 defeat on the final day of the campaign.

Despite the obvious disappointment, Lampard insists he could not be overly critical of his players afterwards.

"Probably the recovery from Thursday - it was difficult for us," said Lampard, when asked about the reasons for the loss.

"It was a big night, the players were tired because everybody at the Club gave it everything [on Thursday]. We had a bit of a body count [beforehand]. We were suffering - players playing with knocks and tiredness levels from the past month, where the Club has given everything. 

"We were in the game in the first half - we had some chances - and, at half-time, I fancied us to maybe create a bit more in the second half. 

"They should have had belief [going into the second half]. We weren't playing so well, we should play here more - we had a bit of freedom. We didn't do that much. I thought we could be much braver on the ball and play a little bit better. 

"The third goal, which is disappointing for us... We conceded three goals from set pieces today and when you do that you know your backs are going to be against the wall pretty much to get results.

"But we found it a struggle for various reasons and I can't complain too much because the players have given so much. 

"It was just that one game a bit far, we knew we were safe and that probably reflects in the result."

Yet another sold-out away section of Evertonians remained in fine fettle throughout the match, with the famous Spirit Of The Blues song, which once again rocketed up the UK iTunes chart this week, heard from the first whistle to last. 

There was also constant support for manager Lampard in the form of chants and flags - and the Everton manager says he is determined to reward their "unique" support with a stronger outfit next term.

"The supporters have been a key part," he said. "They are pretty unique. They do things that go the extra mile and it's rubbed off on the players, without a doubt. 

"We feel for them a bit today in terms of the result but, at the same time, I think they came down with an understanding that the players gave everything on Thursday and that for us in my time is a success. I think the fans feel that, too, given where we were when I came in.

"We need to go away and hopefully give them a team that isn't in a similar situation next season. 

"That's on us. We can affect that and that'll be our job going forward."

When asked on specific plans on how to make positive steps forward over the summer months, Lampard added: "We need to improve in a lot of areas. 

"Rest up a bit, work hard, improve in any way we can with the squad - we'll look at the squad and see if we can get better - and stick together, because we've seen the power of the club when we're together, which we have been since I've been here and for the last five or six weeks, in particular. 

"When we're together and strong and show that kind of passion that every Evertonian has who comes and watches the game, then we give ourselves a real chance. 

"We must stick with that and improve our quality with hard work."