Chelsea drew 1-1 with Irish side Bohemians in the first game of pre-season after giving away the lead in the final minutes.
An early Michy Batshuayi goal looked to have handed Lampard victory in his first match since replacing Maurizio Sarri as head coach at Stamford Bridge.
However, a late equaliser from Bohemians trialist Eric Molloy handed the hosts a famous draw.
Lampard made 11 changes at half time, including bringing on 17-year-old Ian Maatsen.
It will be a lesson for Frank to see players and in a way it will make his mind up
Hasselbaink was impressed with the young Dutch defender but less so with the rest of his team-mates.
He claims Lampard will have some decisions to make over the future of some players after seeing their performances.
“They lost the ball way too easy,” Hasselbaink said on Chelsea’s official coverage of the match.
“Players were having too many touches, sometimes seven, eight touches and it slows the game down.
Jimmy Floyd Hasselbaink has hit out at Chelsea for their first performance under Frank Lampard
Hasselbaink was not impressed with Chelsea’s second-half performance against Bohemians
“It will be a lesson for Frank to see players and in a way it will make his mind up.
“[Moving the ball fast] is his idea of how he wants to play the game.
“The majority of successful teams do move the ball quickly.
“We saw today, especially in the second half, certain players were dwelling a little bit too much on the ball.
“They didn’t have a solution before they had the ball.
Frank Lampard watched his Chelsea side draw alongside his new-look coaching staff
“It might be that it’s pre-season, it might be that they’re not fit yet and it will come.
“For some it might be a little too much.
“That is for Frank to figure out, who those players are and who he will go further with.
“That’s why those games are so important.”
However despite the late equaliser against a team who are midway through their season, Lampard thought it was still a good workout.
He said: “It was a tough game for us, we haven’t been back for long.
Billy Gilmour was one of a host of Chelsea youngsters given a chance by Frank Lampard
“There was a bit of pressure on the lads, we’ve been working them hard so I’m pleased with the outcome.
“Fitness was our issue, we worked them hard this morning.
“I wanted to stretch them a bit and put them under pressure, it’s what pre-season is about.
“The quicker we get to the level we want, the better obviously.
“We wanted to win the game, but it’s not about that. It’s about individuals getting fit and pushing themselves to the limit.”