Lennon had demanded a response after seeing his side slip to a shock home defeat to Kilmarnock on Saturday and believes that the result has put a marker down for the rest of the season.
He told BBC Sport: "I told them 'this time last week you were well motivated, you were in a nice climate, going out [against Barcelona] in the Nou Camp, tonight is different with maybe 15,000 but the attitude has to be the same'.
"I got that. I enjoyed watching my team tonight. That is a marker, I hope, for a concerted period of performances. That is what I am demanding from them.
"The pace we played at was very high and the third goal was magnificent. We were aggressive in our pressing and aggressive in our possession."
Celtic were joined in the last four by St Mirren after they edged past Aberdeen on penalties.