One win in 14 games has left the Canaries four points clear of the Premier League drop zone.
Garrido, on a season-long loan from Lazio, said: "We have to beat Swansea - a point wouldn't be good enough.
"This is the perfect time to play them because they have lost their last three games. They have won the Capital One Cup and they are comfortably placed in the table.
"So they don't need the three points as much as we do. One win in 14 just isn't good enough.
"That's why it's such an important game for us."