The 2-1 win over Stoke on Sunday took Newcastle to 13th - equal tenth - but some nine points clear of the drop zone.
Marveaux - who brilliantly created the winner for Papiss Cisse in injury time - says they are happy to be looking up rather than down.
"It's a big step, it's a big relief," he told the Evening Chronicle.
"It was very important for us - everyone is happy. We needed three points.
"The scenario of the game was good for us. We showed that we can be resilient, and that we don't give up.
"We were in trouble after the penalty, but we found solutions.
"We just have to continue and play as we have been doing. And we have a big game again on Thursday, and then again on Sunday. We have to make sure we're ready for these two games."
Marveaux was pleased to make a contribution against Stoke after coming off the bench.
He added: "That was my role - to create something. When I had the ball I just saw Papiss in the box, so I gave it to him.
"At the training ground, he scores a lot of goals, so we know even if he's not in a good game, he can score at any moment."