The Swiss could have locked up a spot in the round of 16 with a two-goal win over Honduras, but Switzerland played with little urgency or creative flair, and couldn't translate its domination of possession into quality scoring opportunities.
Honduras almost stole a win in the 71st, but Switzerland keeper Diego Benaglio denied an unmarked Edgar Alvarez with a brilliant one-handed save.
Spain and Chile finished even on six points after Spain's 2-1 win over the South Americans in the other Group H match. Switzerland finished on four, and Honduras on one.
The Swiss campaign in South Africa started with a 1-0 upset win over European champion Spain, but the team then lost 1-0 to Chile, and couldn't muster a goal against winless Honduras.
Switzerland went close in the 17th when Tranquillo Barnetta's cross from the left found Eren Derdiyok at the back post, but he headed just wide of the post.
Striker Blaise Nkufo then had two chances just before the half. The first came in the 43rd, when a cross from Derdiyok found Nkufo at the back post, but the striker could only tamely chest the ball across the goal mouth. A minute later Nkufo headed a free kick from Reto Ziegler just wide.
After a tight first half, the game opened up in the second with both teams facing elimination from the competition.
Needing to score, Switzerland coach Ottmar Hitzfeld brought on Hakan Yakin at the break and striker Alexander Frei in the 69th in an attempt to liven up the Swiss attack.
Tranquillo Barnetta had a solid chance for Switzerland in the 60th, finding space in the box only to hit his right-foot shot straight at keeper Noel Valladares.
Derdiyok had a similar chance three minutes later that Valladares easily blocked.
As the Swiss pushed forward in desperation, Honduras threatened on the counter.
The Central Americans should have taken the lead in the 53rd, but striker David Suazo flicked his header wide after clever work by right winger Edgar Alvarez.
Alvarez had his own golden opportunity 18 minutes later on a swift counter, only to be denied by a one-handed reaction save from Diego Benaglio.
 
Diego Benaglio, Stephan Lichtsteiner, Steven Von Bergen, Benjamin Huggel (Xherdan Shaqiri, 78), Tranquillo Barnetta, Gokhan Inler, Blaise Nkufo (Alex Frei, 69), Stephane Grichting, Gelson Fernandes (Hakan Yakin, 46), Reto Ziegler, Eren Derdiyok.
Noel Valladares, Osman Chavez, Maynor Figueroa, Victor Bernardez, Hendry Thomas, Ramon Nunez (Walter Martinez, 67), Wilson Palacios, Jerry Palacios (Georgie Welcome, 78), David Suazo (Danilo Turcios, 87), Mauricio Sabillon, Edgard Alvarez.