The Uruguay international has little doubt the Vicente Calderon side can deal with their star striker's absence and was pleased with the 1-1 draw against Barcelona
The Spain international picked up a hamstring in the first-leg of the Champions League quarter-final tie against Barcelona on Tuesday and was forced to leave the pitch in the opening 45 minutes of the 1-1 draw due to his physical problems.
It's unknown as of yet how long the powerful attacker will be out of action, but Godin feels Atletico have already shown that they are a force to be reckoned with without Costa, too.
"We lost Diego Costa, an important player for us, quite early and you always feel for a colleague who goes through that," Godin told the official Uefa website.
"But we already knew that this group of players is capable of facing up to a challenge like that and we proved it tonight."
Godin then went on to voice his satisfaction with Atleti's performance at Camp Nou and is hopeful they can progress to the semi-finals of the competition.
"I don't think we really suffered much in this game. We put in a monumental effort, each of us, and I'd say we did exactly what we had to do all through the match. This was a very complete performance.
"Taking into account that we were the away team, playing in a stadium where it's so difficult to get anything, we have to be very satisfied with this result – particularly having scored the away goal.
"It leaves the tie totally open and while there are still 90 minutes to play we are pleased with this."
The return at the Vicente Calderon takes place on April 9.