Lester saw his side twice go ahead but for the second home game running they were beaten by a goal in stoppage time.
It had looked good for the hosts when an own goal by Harrison Dunk after just 38 seconds gave them the lead but Alex Whitmore levelled in the 19th minute.
Chesterfield retook the lead when Kristian Denis scored in the 55th minute but Cambridge hit back 13 minutes later through an Uche Ikpeazu penalty.
And in stoppage time, Dennis had a goal ruled out for handball at one end before Dunk won it for the visitors at the other.
Lester, whose side remain in the League Two relegation zone, said: “You are 1-0, 2-1 up at home and we had a game plan we felt would win the game but again it was sloppy mistakes which happen too often.
“We are not being opened up, theshape was good and I think the formation was the right one to play, but we made sloppy individual errors and that’s something you’ve got to learn quickly as a footballer and we have to pull together.
“It’s frustrating of course and I thought we would put the extra man up front and take the game to Cambridge because they haven’t been on a good run and we had a great bit of play to go 2-1 up but we were a bit edgy.
“We are in it together, the staff and the players and we have to take responsibility as well.”
Cambridge’s victory was their first on the road since September, and interim head coach Joe Dunne felt it was a well-earned three points.
He said: “It was a good win and I thought it was a deserved win. We had a really edgy start but I said to the guys on the bench there’s still a whole match to go and we got ourselves back into it.
“They had good moments in the match to put us on the back foot but we made one or two switches that helped and I thought we controlled a lot of the tempo in the second half and they started to look edgy.
“We pushed and pushed to get the winner and we were due a bit of luck and tonight we got a break but overall you can’t fault the commitment of the players to go and win the match.”
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.