The La Liga champions conceded three times in the first 13 minutes, leaving them with an uphill battle at the Mestalla.
And although Mario Mandzukic pulled a goal back before the half-hour mark, Atleti were unable to score again, with Guilherme Siqueira failing to convert a penalty on the stroke of half-time.
"It's hard to take because we're coming from a very nice week, with good games and we were hoping to win, or at least not lose," Godin is quoted as telling AS.
"The first 15 minutes were bad, a bad start that was very expensive.
"It would have been better to have a week to prepare for the match but it's no excuse. We were poor for 15 minutes and they were superior.
"With the penalty we could have gotten back in the game but we couldn't overcome three goals.
"The lack of intensity and concentration cost us.
"We played well, we were superior and we created chances. There's nothing definitive but it hurts to lose. We have to correct the mistakes, draw conclusions and move on."
Atleti lie third in the table, five points adrift of leaders Barcelona.
