The Foxes gained revenge of sorts for last season's dramatic play-off semi-final defeat at Vicarage Road as they put the Hornets to the sword with ease.
It was enough to move second-placed Leicester 10 points clear of Watford, who are now winless in three, and wing-back Anya knows the Hertfordshire outfit must improve ahead of this weekend's trip to Middlesbrough.
"I think a lot of our play wasn't up to scratch," he told the club's official website.
"From the word go we were slow to react, it took us 30 minutes to get into the game.
"I think in the second half we had a spell when we did very well. I had a chance to score that I messed up, Fernando (Forestieri) and Troy (Deeney) had good chances as well.
"From the opportunities side of things we haven't done too badly, but our general play wasn't good enough."
Looking forward, Anya added: "I think we'll keep with the same philosophy. When we lose we try not to get too down and when we win we try not to get to high.
"We're just going to go into training on Monday, the gaffer will have a few words to say, and we'll prepare for Middlesbrough and try to put in a better performance than we have here."