Werner, who Chelsea signed from RB Leipzig in June, netted his first goal for the club on Tuesday night to put the Blues in front against Jose Mourinho’s Spurs.
The Blues wasted a number of chances to extend their lead, however, and were left to ruse their missed opportunities when Spurs’ Erik Lamela equalised late on and sent the tie to penalties.
A total of nine penalties had been converted in the shootout before Mason Mount saw his effort clip the post and sail wide as Chelsea were knocked out and Tottenham progressed to the quarter-finals.
The defeat signalled more disappointment for big-spending Chelsea, who were beaten by Liverpool earlier in the month and dropped points in a dramatic 3-3 draw with newly-promoted West Brom last weekend.
Reacting to the defeat on Instagram, Chelsea goalscorer Werner said: ‘We win and lose together… We will try to make it better on Saturday!’
Chelsea will be desperate to return to winning ways this weekend when London rivals Crystal Palace travel to Stamford Bridge.
Discussing Chelsea’s defeat to Spurs and their Carabao Cup exit, Lampard said: ‘The first half was as much control as you can have in a game of football.
‘I keep saying the same thing but there’s no doubt that if you look at our first-half performance and some of the great stuff we did, that’s going to keep coming.
‘To sustain that for 90 minutes with the fitness we’ve got is hard – you can see they were dead on their feet at the end.
‘Tottenham had an extra two weeks of pre season. That’s a tough challenge but I can’t be unhappy with a lot of the performance.’
Germany striker Werner scored 95 goals in 159 appearances for Leipzig before joining Chelsea for £47.5m.