Griezmann admits Atletico will have to suffer away at Dortmund
Diego Simeone's side beat their German visitors 2-1 in the quarter-final first leg on Wednesday but after dominating the first half their advantage could have been bigger.
Rodrigo De Paul and Samuel Lino netted in the first half but Sebastien Haller hit back in the 81st minute.
Dortmund hit the woodwork twice in the final stages as Atletico clung on for victory.
"In the second half they had the ball and pegged us back, we suffered quite a lot," Griezmann told Movistar.
"We will have to suffer there - we've got to go for the game and win it, we've got the quality to get to the semi-finals and beyond."
Griezmann spoke to media with an ice pack strapped to his ankle but said he thought he would be fine after some treatment and rest, after coach Simeone said he had been playing through a niggle.
"We've got the best physios in Europe to recover well, I'm doing very well, trying to help the team," he said.
Griezmann said he was expecting strong support from Atletico fans for the return in Dortmund next Tuesday.
"Atletico supporters travel, they prefer to travel for the team than to buy things they need for their homes, I'm so proud to be at this club," he added.
"Maybe it didn't look great (in the end) but it's a win in the quarter-finals and it's very important to win."
Simeone, who recorded his 50th win in the Champions League as a coach, agreed with Griezmann about the second leg.
"I view (the second leg) as very tough, difficult, it's huge," said the Argentine.
"We have to be prepared for what awaits us."