Although the Reds took the lead through Sadio Mane, the goal should have been ruled out as James Milner - who provided the cross for his team-mate to score - was in an offside position in the build-up.
West Ham quickly equalised and Declan Rice's free header could have given them a half-time lead, while Noble went close to scoring late on for the hosts.
Divock Origi almost won it in added time for the visitors, yet Noble hailed a fine performance from Manuel Pellegrini's side as they bounced back from three straight losses in all competitions.
"January was a bad month for us," Noble said to Sky Sports.
"We defended fantastically well and probably deserved to win tonight. You can't play man to man against Liverpool and out-pass them. You have to keep your shape and stop them.
"We scared them. You have to do that against the top teams. I'm just gutted we didn't come away with the three points.
"We're gutted in there because the goal was clearly offside. We scored a fantastic set-play and didn't manage to get a second goal."
Liverpool boss Jurgen Klopp was quick to laugh off Noble's assessment, though, saying that he saw a poor performance, not a scared team.
"I like that really. I would wish for all West Ham fans that Mark Noble and his team would scare more teams and not only us tonight," Klopp said.
"I don't know him really well, so I don't know why he speaks about us after a game like that. They defended well, that's true. They didn't scare us.
"It's a normal away game. We won away games when we played worse than tonight and nobody spoke about it. Last year we won at Crystal Palace 2-1 with two offensive situations pretty much. Tonight we had more.
"They have quality - no doubt about that. Why they don't get results more often, I don't know. But tonight they had a result, 1-1, but I didn't see that they scared us."
But while Virgil van Dijk acknowledged defensive alterations have hampered Liverpool, he said it was no excuse for consecutive 1-1 draws, results that mean a Manchester City win at Everton on Wednesday will see the champions take over at the top.
"It's tough but they were decent and defended well. It could have been a lot better," Van Dijk told Sky Sports. "It is what it is. We have to keep going.
"That [set pieces] is their strength, they practice on it a lot. When you have a back four who don't change it is maybe a bit easier. But we have enough quality to fill it.
"What can we do? We take it game by game. We're still top of the league. You need to enjoy the pressure. You can also be playing for nothing. We're still in the race. We go again."