Goals from Beto and Kiernan Dewsbury-Hall cancelled out Igor Thiago’s brace for the result at the Gtech.
Moyes said: “We've got a bit of maturity about us and I think away from home we've shown that in some of the games.
“We had to today again, Brentford's not an easy place to come and get a result and we had to show a bit resilience and stick at it and believe that there might be a chance."
On their injury-time equaliser, the Scot also said: “It says loads and loads about what they're like. They're really good lads, trying to fight for every opportunity they can.
“We don't want to go behind, and sometimes when you're fighting, sometimes you can open up and end up going two down.
“But we stuck at it, we didn't concede again. It gave us an opportunity to get back in the game.
“We've done a really good job away from home in the main, probably with our points, which we've picked up on the road.
“We've got three more times we've got to come to London, so we'll need to find ways of picking up more points when we come down here in the future.”