The legendary midfielder suffered a second straight defeat as Chelsea boss on Wednesday night.
Chelsea were beaten on penalties in Istanbul by Liverpool after drawing 2-2 after extra time.
An Olivier Giroud goal and a Jorginho penalty cancelled out a double from returning Liverpool striker Sadio Mane.
After both sides had scored four penalties, it was down to sudden death, with Abraham needing to score to keep the Blues in the shoot-out.
But the youngster’s penalty was too weak and was aimed low, allowing Adrian to save the effort with his feet after diving to his left.
Abraham was visibly upset after his miss cost his side the trophy, but Lampard insisted that he had no need to be hard on himself.
In his post-match press conference, the manager revealed that he drew on his own experiences when speaking to the striker afterwards.
“Yeah I told him not to worry,” he said. “The fact that he is confident enough to stand up and want to take a fifth penalty [is impressive].
“I have been there, missed penalties. Anyone can.
“I want the confidence of a young player to stand up and want to do that.
“I said not to worry. He will come back stronger.
“It is part and parcel of being a player in the top level, which Tammy now is.
“These moments come. We have to be very supportive of him.
“His team-mates were, I certainly am. That is football.”
Abraham is expected to start against Leicester City on Sunday having been dropped to the bench in favour of Olivier Giroud last night.