Glasgow currently occupy second place in the GUINNESS PRO12 table after beginning the season with five successive wins before last weekend's trip to Ulster.
The Warriors fell 29-9 for their first loss of the season and don't return to GUINNESS PRO12 action until the end of the month as Europe takes centre stage.
And lock Swinson admits simply doing well in the GUINNESS PRO12 - they reached the final last season - cannot be deemed good enough at Glasgow.
"Losing is part of professional sport. Anyone who thinks they are going to go through the season undefeated and win every title going is delusional," he said.
"It is how you respond to defeat. This is the first round of a new European competition and we want to show something that teams in the PRO12 have realised for a number of years - that Glasgow are a good side and we now want to show that to a wider audience."
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