Ottmar Hitzfeld's team frustrated their illustrious South American opponents for long periods of an attritional contest before Angel di Maria clinically broke the deadlock with an extra-time winner after 118 minutes in Sao Paulo.
Lichsteiner chased back in vein having been dispossessed by Argentina substitute Rodrigo Palacio, who set Lionel Messi on a driving run to tee up Di Maria.
While shouldering that responsibility, the Juventus man insisted his team-mates did not deserve such a fate in the last 16 clash.
"Switzerland deserve praise for a great performance and we didn't deserve to go out like that," he told Sky Sport Italia.
"We proved that we are a very good side and it was a wonderful game for us until that moment.
"On the goal I lost the ball after a challenge and they were able to run in on goal.
"We were punished when the match was practically over. It's such a shame."
