Watkins’ fourth Premier League goal of the season earned Villa their fifth win in seven matches, at the end of the week in which they sold top scorer Danny Ings to West Ham.
That put more focus on Watkins but the 27-year-old responded by bagging the winner when he headed home 13 minutes from time.
Emery, who wants to bring in another experienced striker to provide competition, said: “It is a good pressure for him.
“If he is feeling it, he can also feel our support and his team-mates support. He has responsibility as well to do his work and if he is scoring he can be feeling better and take confidence.
“We are not giving him the sole responsibility. Other players like Leon Bailey and Buendia and Ramsey get in the box and can score. His goal today was very good for him, for the team and we got the three points.”
Though low on quality, the match was incident-packed with play halted for around 10 minutes late in the first half when a drone flew into the stadium.
Southampton skipper James Ward-Prowse then thought he had broken the deadlock just past the hour mark only for the goal to be ruled out following a VAR check, with Mohamed Elyounoussi adjudged to have fouled Jacob Ramsey.
Emery said: "I respect 100 per cent the VAR. I didn't move one hand when the refere was watching it for us or for them.
“If he decided then I am of course accepting it. Today it is for us, sometimes it will be against us.”
Villa have now won five out of seven Premier League matches under Emery – including all three away from home – and are just three points behind sixth-placed Brighton.
Emery continued: “Today was a key match because we were near the bottom two months ago and every team is pushing.
“I think it is a key match, in terms of how we can break from where we were. Now, I am looking at the table, we have 28 points. The difference with the players is big.”