Koke scored the only goal of the game after just five minutes to seal a 2-1 aggregate victory for Diego Simeone's men and Atletico could have won by a far more comfortable margin as they also hit the woodwork three times in the opening 20 minutes.
"At the start, the game went in Atletico’s favour,” said Martino. “They were playing direct and winning the second balls. It wasn't that we lacked intensity, but we couldn't put four or five passes together.
"There was a big difference between the sides in the first 20 minutes, but after that both teams had their chances."
Defeat means Barca have still not managed to beat Atletico in five meetings this season.
A common factor in all those games has been Lionel Messi's inability to make an impact as the Argentine was again well-marshalled by Atletico and kept on the fringes of the game.
On the other hand, there was a completely different set of emotions for Simeone as Atletico's incredible turnaround under his tenure continues.
However, he insisted Atletico's inexperience will ensure they remain underdogs in the semi-finals.
"We maintain the same humility,” said Simeone. “We understand that the other teams have been there far more than Atletico Madrid.
"We are there 40 years later and we believe in what we are doing. We want to continue being competitive as was our intention at the start."
Champions League wilderness looms for United
As Manchester United's players trudged from the pitch at Bayern Munich, it was with the knowledge that they will not experience the Champions League again for at least 17 months.
United are seven points below the top four in the Premier League, and with only 15 points still to play for, next season is almost certain to be their first without Champions League football since 1995-96.
And once banished from Europe's top table, clubs can struggle to return.
"It's hugely important we get back in it as soon as possible," said defender Phil Jones, after Tuesday's 3-1 loss at Bayern completed a 4-2 aggregate quarter-final defeat.
"United need to be in the Champions League. Nights like these do not come around too often. They are the ones you look back on and think, 'What a time that was'.
"You want to play against the best and you want to test yourself against the best."
While Jones, at 22, can reasonably hope that he has not played his last Champions League game in a United shirt, the same cannot be said for some of his older colleagues.
Captain Nemanja Vidic has already agreed to join Inter Milan, while fellow defenders Rio Ferdinand and Patrice Evra are also expected to leave in the close season.
Ryan Giggs, meanwhile, is yet to announce whether he will extend his contract.
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