The Hammers captain was delighted to see his side hold out against a spirited Hoops fight-back to secure their first away win since returning to the Premier League
The Hammers raced into a first-half lead thanks to goals from Matt Jarvis and Ricardo Vaz Te, and held onto their win despite the Hoops' fightback in the second period and Adel Taarabt's stunning goal.
Nolan told Sky Sports: "It was absolutely vital. Absolutely delighted with the win today.
"They made us work for the win in the second half. It was a fantastic first-half performance, the second half I thought we dug in and we could have won it by more in the end really.
"We knew at some point they had to make changes, we had to be ready for that and I thought we dealt with it well, which Nolan was proud with as he claims his side showed their quality.
"It was a great goal [from Taarabt] but I thought after that we responded well, we dug in, they had the man sent off which helped us, but I thought overall we were well deserving of the win.
"Tonight we proved we are tough to beat and we have quality."