The Warriors, who had already lost at Rodney Parade earlier this season, had registered just one victory in the Magners League and Lineen was full of praise for a team he admitted was low on confidence.
"The overall feeling is one of relief. We've been getting closer and closer to that result over the last few weeks so to get the result is very satisfying," said Lineen.
"We managed to get the tempo of the game up and we turned some of the pressure into points but you could see how anxious the players were with some of the chances we missed.
"This win makes a huge difference to our confidence going into our next match with our defence the way it was and the way we controlled the contact area, we have had a big boost.
"We have to be happy with that performance because we have been working hard over the past couple of weeks and we knew that it would come."