Wales ended an eight-match losing streak and put their Championship back on track with their 16-6 victory over France in Paris.
But Hibbard insists the win is just the beginning of what Wales aim to achieve in the tournament.
"The pressure is not off us yet," said Hibbard. "It's a good starting point.
"It's put to bed a lot of demons and given us a big confidence boost.
"The coaches have been telling us that we haven't gone from being a good team to a bad team overnight.
"We are happy with the result but there is plenty more to come. It's a relief to have ended the run of eight defeats but the pressure is not off us yet."
Hibbard was thrilled as Wales got back to winning ways in his first Six Nations start and he paid tribute to the pack, who matched France's giant eight.
"The boys put in a hell of a performance. We knew that France would be a big, physical team and we knew that we would have to go all the way to the 80th minute.
"Their pack was huge. The starting eight and the players coming off the bench seemed to be even bigger - it was like replacing tanks with tanks.
"But I thrive in that sort of battle, the bigger they are the harder they fall.
"We all put in a hell of a shift and didn't allow their eight to dominate us."
And having played his part in the hard-fought victory, the Ospreys hooker is desperate to hold on to the number 2 jersey.
"I would have liked to have done more things around the park, but I thought it went pretty well for my first Six Nations start," added Hibbard.
"Hopefully the coaches will let me build on it and I can keep putting in good performances."