Pavel Pogrebnyak capitalised on an error from James Collins to net the winner in the fifth minute and the Royals then held on with Hammers sub Ricardo Vaz Te spurning a late chance to equalise after Reading midfielder Jem Karacan had rattled the bar.
McDemott said: "It's a great relief and I thought it was a real resilient performance. We had to stand up to West Ham today and I thought we did that.
"It was a great finish by Pavel in the first half and Jem's hit the bar in the second half. I thought we needed the second goal but I thought we managed the game well in the last 10 minutes.
"They have had that one opportunity that they didn't take so every point in this division is precious. We have realised that and it is a good win for us today.
"We are so pleased today because it was a great, great show of strength and show of unity at the club. Our fans will go home happy tonight because they have got the three points and that is the most important thing for us."
When asked what had changed over the past few games, McDermott said: "A tactical switch, a mindset switch, we have to do what we have to do to pick up results and I have been fortunate in the last three years that I have got results - we are in a results business whatever league we are playing in and we need to keep that going.
"Last year was a miracle to win the Championship, I don't know how many points we are behind but all I know is that we have got to try and win the next game."
McDermott was also delighted to see Pogrebnyak net his first goal since October.
He added: "They've made a mistake but he has still got to finish it. It was a top-class finish and Pavel can finish. He has proven that and if we can get him the service he can finish."