Swansea maintained their 100% record in Group A with a 1-0 victory but Routledge admits that the hosts were severely tested by their Swiss opponents.
"They battled hard and it was a gritty win and we're happy to have the three points. I thought [the ball] was going in, I left it roll as long as I could but I tapped it in," the winger told ITV Sport.
"It shows we have massive character. We can knuckle down if we need to and play if we get the chance."
Swansea lead St Gallen and Valencia by three points at the top of the group.