Mario Lemina's goal on the stroke of half-time, after the Gabon midfielder had dispossessed Mohamed Salah, inflicted a sixth successive Premier League home defeat on the Reds and saw Parker's side draw level on 26 points with 17th-placed Brighton.
"It's a big win. There's a lot of emotion and I am very proud," said Parker.
"I am happy for the players and the team because they got nothing short of what they deserved. There was a resilience and real attitude to keep the ball out of the net and defend."
He added: "In the first half I thought we were fantastic. We created numerous chances and we stuck to the plan in terms of how we wanted to cause them problems.
"The main thing coming into the game was 'can we put our stamp on it?' - easier said than done of course.
"We deserved this result and we have deserved better results over the last few weeks."