David Silva double and David Villa strike end Scottish hopes of ending an exile from major tournaments since 1998, but coach believes his team are improving
The Scots went into their final Euro 2012 qualifier in Alicante knowing that if they matched the Czech Republic's result in Lithuania, they would be assured of a play-off spot and finish second in Group I.
However, an early goal from Manchester City star David Silva soon put the visitors in trouble, and as the Czechs eased to a 4-1 victory in Kaunas, the Scots spent much of the match against Spain chasing shadows.
Levein, however, refused to be too downbeat as Scotland's absence from a major tournament finals extended to a minimum of 16 years by the time of the next World Cup.
"The result is disappointing," he said to BBC Sport. "We don't like to lose but as I said to the players after the game, this is as hard as it gets.
"To come to the home of the European and world champions, play them in their own backyard, is an extremely difficult thing to do.
"We knew we had to be at the top of our game and they maybe would come down 10 or 15 per cent - well, unfortunately for us they played pretty close to maximum tonight. When they are like that they are very difficult to play against.
"I have to give credit to our guys though, they stuck at it in the second half and on another night could have had three or four goals."
Levein stuck to his 4-5-1 formation until the Scots trailed 3-0 early in the second half, and the switch to 4-4-2 following the introduction of Blackburn Rovers striker David Goodwillie - who scored a penalty with his first touch - coincided with the best passage of play for his side.
But the manager batted away any suggestion that he could have employed a more attacking strategy from the start.
"It is easy to say that in hindsight," said Levein. "I made the changes because we had nothing to lose.
"We set out in a pattern that we have played in and played well recently and it is something that I'll stick by.
"It is good to know that if we need to change the game then we can put two strikers on.
"But we learn every game, I believe we're improving all the time, including in this game, where I thought we did some things exceptionally well. There are some greatly encouraging signs to come out of this for me."