Reds skipper Jordan Henderson was dismissed before Firmino’s third and will now miss next week’s Merseyside derby.
Liverpool are on 33 points – a Premier League record for the club at this stage of the season and have conceded just five goals.
“That’s just the confidence that we have got at the minute,” the England right-back told the club website.
“We are not going to concede that many goals – and the forwards can score the goals. As long as we keep that belief then I’m sure we will keep getting these types of results.
“In the first half we found it quite tough but we managed to keep them out and we knew if we kept going we would get a good chance at goal ourselves. That came in the second half and the later it went on, the better it was for us to break them down.”
Alexander-Arnold doubled the lead before Firmino headed in with a minute left.
“Before the game me, Hendo (Henderson), Millie (James Milner), everyone was joking about who would take it (his free kick),” Alexander-Arnold added.
“I think Hendo wants one so he stepped up with the ball in his hand. Then he passed it to me because the gaffer said before the game that me and Shaq (Xherdan Shaqiri) would be on them.
“So that’s why when you look back at it, me and Hendo had a little moment together when we celebrated as a bit of a joke.
“It’s always good to be able to score and contribute to a win; we were happy to get the win first and foremost.”
Watford sit ninth in the table and are winless in three games but boss Javi Gracia remains unconcerned.
He said: “I feel in all the games we have played so far we have competed well and in the last two games there were some decisions that made us feel a little bit unlucky.
“If we keep the same attitude and way of work every day I don’t have any doubt we will be able to win.”