Northern Ireland defender McAuley, who scored against Portugal and Luxembourg during the international break, headed in Chris Brunt's stoppage-time corner for the Baggies' first goal of the Barclays Premier League season in Saturday's 1-1 draw at Craven Cottage.
"It's not been too bad a week for me," McAuley said on wba.co.uk.
"Some of the lads asked if I could do three in three. I've done that so now I might have to try to score four in four.
"It hung up quite nicely and I just had to get my head on it.
"I knew if I got it on target it had a chance of going in (and) it was great to score in injury time.
"It gives you an extra buzz when you get a point in an away game in the last minute.
"We needed it. It was important we got off the mark. It's a monkey off our back."
The Baggies climbed above Sunderland and the Black Cats are their next opponents.
"It gives us a platform to build from going into next week's home game with Sunderland," McAuley added.
"We need to take the positives from this game and grow in confidence."
West Brom boss Steve Clarke has plenty of confidence in his charges and expects his side to challenge in the top half of the Premier League again this season despite their slow start.
The Baggies finished eighth last term but have made a number of summer signings to strengthen the squad's depth.
"There's more to come," Clarke said.
"Three or four players came late in the window. We need a little bit of time to gel. There were good signs there that we're going to be a strong force in the Premier League again this season."
Victor Anichebe made his West Brom debut following his move from Everton and combined well with Nicolas Anelka, but neither was clinical when it mattered.
Clarke added: "They showed good signs, they linked up well at times. Victor showed what he can do for us. He's a different type of striker to Nicolas, big strong, can hold the ball up.
"They both got into really good positions where on another day where confidence is higher they would both have scored.
"Good signs for the future."
On-loan Marseille midfielder Morgan Amalfitano also started, but a third deadline day arrival was absent in Stephane Sessegnon.
Clarke hopes the work permit issue which kept the Benin forward out of the Craven Cottage fixture will be resolved imminently and that Sessegnon will be permitted to play against his former club Sunderland next weekend.
Shane Long is again likely to be absent with a knee problem.
Clarke said Long was "doubtful for next week's game".
The Scot added: "Beyond that, I don't think the diagnosis is any worse than that. It's not something we're looking at as a long-term injury."
Fulham manager Martin Jol was the target for a vocal minority of fans frustrated at a sixth home game without a win.
The last home win at Craven Cottage was on April 1 versus QPR.
Fulham were without on loan Aston Villa striker Darren Bent, but Jol was satisfied with the display, apart from the inability to add to Steve Sidwell's opener and the late lapse which allowed McAuley to score.
"I don't think we missed anybody," Jol said.
"I think we played better than before, the balance was good. I thought (Pajtim) Kasami did very well, the balance looked good.
"I left one or two players out and gave Kasami a chance again because he did very well when he played.
"We did okay, but the only thing is we looked a bit tired at the end. For a lot of players it was their third game in seven days, but that is not an excuse not to score a second goal."