The game at St James' Park was deep into injury time when Moussa Sissoko crossed for Georginio Wijnaldum to cement the win and finally allow McClaren to believe a massive three points was his amid speculation that he might have only two games left to save his job.
Asked about his emotions when Wijnaldum struck, the 54-year-old said: "Sheer relief because even then I thought with a minute to go, we could likely concede two with the way we go.
"It was relief because you know Liverpool, they have got quality players in any moment and that could have spoiled it, like (against) Chelsea, conceding just at the end.
"It could have spoiled it, but it didn't today. We'll enjoy this for 24 hours, Tuesday morning we will review it, bounce heads off the wall again and get back to work and get ready for next week.
"Now we have got to take that on. We are not getting carried away, we have a lot of work to do. People say, 'Where do you solve it?' You only solve it on the training field, you can only solve it through hard work, and that's what the team got back to today."
The Magpies ran out knowing they would have to improve dramatically upon woeful performances in defeat by Leicester and Crystal Palace in their last two games, and they did just that as they served up a committed and resilient display against a side who blasted six past Southampton in midweek.
Their efforts were rewarded by a stroke of good fortune when Wijnaldum's 69th-minute shot was deflected over keeper Simon Mignolet by defender Martin Skrtel, and - having seen the visitors get the rough end of a tight offside decision to rule out a potential equaliser by Alberto Moreno - the Dutchman made sure in the 94th minute.
McClaren said: "It was a deserved win. We looked nervous at the beginning, but we said before the game the one thing we had to do was out-work Liverpool and if you work hard and you out-work a team like Liverpool, you have got a chance of winning.
"Hard work, then you get the luck, so I think we deserved it. We grew into the game and we showed what we are capable of doing. We hope that's the lightbulb moment that turns it around and we do that week in, week out.
"We might not get results, but it will certainly keep the crowd with us and certainly keep the spirit and give us a chance of picking up points."