A 1-1 draw with Newcastle on the final day concluded a miserable season for Chelsea, despite the huge transfer spending of their owners in the past two windows.
Lampard - whose interim spell in charge is now over, with a record of just one win from 11 games - predicted a huge challenge is waiting for his successor, admitting that standards have dropped at the club.
Pochettino has signed a contract with Chelsea and is expected be unveiled as their next permanent boss in the near future - but Lampard says the players will have to raise their level and attitude significantly for his appointment to lead to improvements.
Super Frank. 🎶 👏 #CheNew pic.twitter.com/7r2g3rXzTM
— Chelsea FC (@ChelseaFC) May 28, 2023
"I'm a big fan of Pochettino as a manager, I think he's a very good manager," said Lampard. "But it's not about which individual it might be, it's about getting the right high level of manager.
"Pochettino's history tells you he works at clubs of this sort of level and then letting him get to work with the players he creates a solid identity in a team that can win more games. Those things aren't always overnight things, so we have to be careful with expectations a little bit.
"There's a lot of work to be done. That's my synopsis after six weeks, the basics that I keep talking about - standards are so relevant to this club at the minute. Standards collectively have dropped - I can be honest about that as it's my last game and I might not see some of them that much anyway!
"Standards as a collective for a club like Chelsea have to be at the maximum or you won't be physically competitive enough, or you won't be able to play at a high level, high speed the Premier League demands.
Honours even this afternoon.#CheNew pic.twitter.com/OVDoAmZnjg
— Chelsea FC (@ChelseaFC) May 28, 2023
"If you're not together in the dressing room and vocal in the dressing room, and driving each other and competitive because 'I want your place and you want mine'… Every top team has to have that.
"When I came in, very quickly I could see that wasn't there enough. Of course a very good manager can help that but everyone has to take responsibility."
One of the major challenges of this season, says Lampard, has been the excessive size of the Chelsea squad, after 19 players were brought in for a £600m outlay. That has led to big-name players being left out of matchday squads or feeling sidelined, impacting the morale of the group.
Trimming down that squad, improving the fitness of the players who remain and instilling a more aggressive, winning attitude in the group will be key objectives for Pochettino, says Lampard.
"When you're Chelsea and you have a season like we've had there are obviously lots of things to improve," he said.
"The next manager will need a pre-season. We're not physically competitive enough, that's a strong opinion I have.
Mauricio Pochettino has finally signed the contract as new Chelsea head coach after verbal agreement reached 2 weeks ago. 🚨🔵✍🏻 #CFC
Official statement ready, he's starting his job as Chelsea manager next week.
Contract will be valid until June 2026.
Here we go confirmed. pic.twitter.com/7BaBpimsFm— Fabrizio Romano (@FabrizioRomano) May 28, 2023
"The new manager can get the squad into the place he needs it to be - the squad has been too big and that has been the biggest challenge, coming in to work with players who for whatever reason are disillusioned. Those situations can be sorted out now and they need to be.
"Some of the players have been mindful of
"The dressing room was pretty quiet
"They have to take responsibility for this season but it's up to them to go and show the pride and dedication it needs to be a Chelsea player."