Watkins set Villa on their way to a 2-0 victory in Gerrard’s first match in charge on Saturday when he fired home in the 84th minute.
The 25-year-old, who made his international debut in March, was omitted from Gareth Southgate’s most recent squad following an indifferent start to the season.
Gerrard said: “I know Ollie has got big aspirations and dreams of being involved in the England set-up so that goal, finish and performance will do him no harm.
“I’m sure Gareth (Southgate) will see that. Gareth knows this football club extremely well but he (Watkins) has got to fight.
“There is a lot of competition there for places and it’s my job and the staff’s job to give him every bit of support he needs.
“That was a world class finish, without a shadow of a doubt. With the score 0-0 and the first goal the most important, it was just pure quality.”
Gerrard also heaped praise on Tyrone Mings after the Villa skipper capped an impressive performance with his team’s second goal.
Mings has also experienced a difficult start to the season and had been dropped by former boss Dean Smith for Villa’s previous home match.
Gerrard said: “It is none of my business what happened before I came in the door and I said to all the players, Tyrone included, that’s not important now.
“What is important is the focus and the attention moving forward, a fresh start for everyone and a re-set if you like. Tyrone showed great leadership skills this week on the back of an international break.
“He has come in with a positive attitude, he helped lead and his individual performance was worthy of being captain of his club.
“He just needs to keep continuing that. He needs to be a pillar in the dressing room for me and help us drive the standard up of this football club.”