Kembali
The Spanish side celebrated their first-ever win on Scottish soil in their 55-year European history, with their debut also being in Scotland, against Aberdeen.
But with a continued boycott from the Green Brigade and plenty of empty seats, Parkhead was around 12,000 short of its full capacity for the tie.
Celta Vigo brought their biggest-ever away European support of 3,000 loud and noisy fans and Rodriguez - who netted both goals in their comeback win - reckoned the Spanish fans made it sound like the game was being played at their Estadio Municipal de Balaídos ground.
He said: "I don't score many goals, so to score two here at this incredible European stadium was amazing for me. Our fans were a big help - they were crazy and were even waiting for us when our bus pulled up. It felt like we were almost at Balaídos.
"We appreciate them coming all the way here, even though it's a bit chilly in Glasgow, and we're looking forward to the next match with all our fans who couldn't be here today, so we can give them another three points.
"It was a party in Glasgow for them."
Rodriguez hadn't previously scored for 18 months, before he netted in La Liga at the weekend against Alaves before he grabbed his brace against the Hoops.
And he insisted Celta deserved it. He said: "In the first half, Celtic created almost nothing, so for them to score the first goal was quite a blow for us.
"But we managed to recover and continued playing as we did in the first half, and luckily, the goals came.
"I am a defender so I am not used to scoring goals, so to get three in my last two games is unbelievable for me."