Despite fielding a strong starting XI - which included the likes of Jordan Pickford, Dominic Calvert-Lewin, Anthony Gordon, Alex Iwobi and Michael Keane - Everton found themselves three goals down after just 36 minutes.
Emanuel Reynoso converted an early penalty, before James Tarkowski doubled that advantage with an own goal. Luis Amarilla scored a third, while Abu Danladi's second-half effort completed a memorable win for the MLS side.
After the match, Lampard warned his side that they must improve if they are to avoid another relegation battle.
He told the club's website: "The players have to work and understand we were in a relegation battle for a big portion of last season.
"We had an amazing night [against Crystal Palace] and an amazing run…but, as soon as that finished, I put it to bed very quickly, so the players have to put it to bed as well, because we were in that fight for a reason. And if we don't want to be in that situation again, they have to better and I have to be better.
"As a club, it [the Minnesota game] reinforced the situation in terms of what we need to do with the squad, because it has to be stronger than what we saw tonight."
Everton have done little business over the transfer window, with Tarkowski being the sole addition to the first team. Meanwhile, the departure of Richarlison has undoubtedly blunted the Toffees' attacking options.
Lampard added: "When you think of where we were last year, we have lost a big player in Richarlison…we wish him well, but our club now continues.
"We know there is a void in forward areas, we are short in numbers there. Also, through the team, there are things I want to strengthen, and I can be honest about that, because a club like Everton has to have a competitive squad.
"The players must be up for the fact they have to fight to play in the team. For me, that starts on day one of pre-season and ends at the end of the season.
"That's the disappointing thing tonight for me - the lads have trained well and trained hard out here but that performance [against Minnesota] should give them a lot to think about on the plane home, because it's certainly given me a lot to think about."
Everton, who also lost their first pre-season clash against Arsenal, take on Blackpool in their third warm-up game on Sunday.