Gareth Bale's first-half penalty had put Wales on course for a victory that would have hauled them back into contention in Group A.
But late goals from Dejan Lovren and Eduardo gave the visitors a 2-1 win at the Liberty Stadium, leaving Wales 10 points adrift of pacesetters Croatia and Belgium with just 12 available, effectively ending their World Cup dream.
As with their Euro 2012 qualifying campaign, Wales have improved after a poor start but it has come too late to salvage hopes of reaching a first major tournament since 1958.
Wales will now target a third-place finish in order to give themselves a better seeding ahead of the 2016 European Championship, where 24 teams will qualify.
Wales have not won the opening two games of a campaign since they narrowly missed out on a place at Euro 2004, and Myhill knows the Dragons need to start qualification stronger than they have managed since.
He said: "We could not have had a worse start to this group. We played Belgium, who are the strongest side in the group, and then we had the heavy defeat in Serbia which no-one in football saw coming. That was a one-off and it will not happen again.
"But we need to stop giving ourselves these massive mountains to climb if we want to qualify for a major finals. We have to start better than we have.
"Now it is vital for us to finish as high up the group as we can to get a better seeding for the next group. We know that, we have been around this long enough to know that, so I am sure we will keep plugging away."
As Wales faded after a first half which saw them produce their best half of the campaign to date, Myhill was forced to make a string of excellent saves to keep the Dragons' lead intact.
The best of the bunch was his acrobatic effort to tip Darijo Srna's drive round the post after it took a deflection right in front of him.
But he was eventually beaten by Lovren's fierce strike. Myhill had seemed set to get behind the shot, but admitted he had been beaten by its movement through the air as he failed to get anything on it.
He said: "To be honest the minute it left his foot I was moving to my right and then I heard the net ripple.
"It is ridiculous the amount they can get the balls to move these days and I am disappointed I could not get anything on it.
"It was way too good for me, I saw it leave his foot and that was it, it was on its merry way. I'm gutted I could not keep it out, but sometimes these things happen."