Wilkins, in charge for the game before new manager Guus Hiddink takes control on Monday, changed to a 4-4-2 formation after Watford went ahead and the Blues never looked back as Anelka took his tally for the season to 20.
"Yes, we had a scare but overall I think our performance merited a victory and we got it," said Wilkins.
"We are creating numerous chances but we are not putting the ball into the net. But that will come.
"I was delighted with the way the guys persevered. It is never easy when you go a goal down to a team in a lower division, it is extremely difficult.
"But we showed a tremendous amount of character to come back and it culminated in a lovely hat-trick by Nic.
"People keep saying it has been a difficult season for us. But we are now through to the next round of the FA Cup, we are still in the hunt for the Premier League and we are still in the Champions League. I don't think you have seen the best of us yet.
"That is still to come. When we get lady luck on our side I think you will see us start giving a few teams a good hiding.
"Nicolas has done exceptionally well but that's down to a lot of hard work by the player. He is not the most vocal person on the planet but he works hard on his game and is a wonderful finisher.
"Guus has been in the dressing room to congratulate the boys. He is delighted and thrilled and knows he has got a wonderful group of players to work with. He also came in the dressing room before the game to wish the guys the best of luck.
"I told Guus what the team would be and he just said get on with it."
Wilkins brought Didier Drogba back into the starting line-up after taking the Ivorian aside for a heart-to-heart chat during the week.
"I had a talk with Didier, a little one-to-one. As soon as the board said I would be taking this game, I had a gut feeling about Didier.
"It's been a difficult season for him, he's been in and out. It has been tough for him but he is the type of guy who I thought would work better from the start than coming off the bench.
"He did respond and it was nice to see the big man back. He is a delight to have in the dressing room because he is extremely vocal."
Beaten Watford coach Brendan Rodgers, Chelsea's former reserve team boss, was extremely proud of the way his players fought against one of the top teams in the country.
Rodgers said: "I thought we were outstanding in relation to the world class squad we were playing against.
"Right up to the end it could have been two-each but instead that little bit of quality came through and Nicolas got his third.
"I am very proud of the players and the supporters. The players are improving all the time. With 20 minutes to go I was thinking 'here we go' but then I should have known better because I have worked with these guys and they are top players."
The only disappointment for the Watford coach came as he tried to replace Will Hoskins with John-Joe O'Toole. The failure of referee Mike Dean's ear piece cost them dearly.
"I am a bit disappointed I have got to say with the referee," said Rodgers.
"We were trying to make a substitution but Mike Dean's ear piece wasn't working, so we could not get him on.
"We got him on but it was too late as they scored their first goal. We could not get the message to the referee and that was the only disappointment really, apart from the result.
"It got to one-each and they are galvanised by it, but hopefully this result will push us on for the rest of the season.
"It would have capped Jobi McAnuff's night if he had equalised in stoppage time but I am very proud of the way all the players went about the game.
"I really hope that Chelsea now go and push on this season. They are a brilliant club who get a lot of stick from various areas."