England were denied what looked like a clear spot-kick when Harry Maguire was grabbed by Rouzbeh Cheshmi early on in their 6-2 win over Iran on Monday.
The VAR decided not to intervene but later alerted the referee to a tug on a shirt in the England box which resulted in Mehdi Taremi scoring a last-gasp penalty, while a similar offence resulted in a spot-kick in Argentina's shock defeat to Saudi Arabia on Tuesday.
FIFA referees committee chairman Pierluigi Collina had singled out England during a pre-tournament briefing - also open to the media - showing a clip of Kalvin Phillips blocking to create space in the box for Maguire to score in England's 5-0 World Cup qualifying win over Albania last year.
The Italian said such a goal would be disallowed at the World Cup and Southgate has been left with concerns about the potential ramifications of England being the team highlighted ahead of the finals.
Speaking after the Iran win, Southgate said he was concerned his side could miss out on penalties if the pre-tournament briefing clouded the judgement of officials.
Pickford, who was beaten by Taremi's late penalty, wants England to still be treated fairly.
"It got brought up in the referee's meeting which we were involved in but hopefully we get the fair side of it," he said.
"It's never going to be perfect. You're never going to be happy all the time with VAR decisions but I think Harry's one could have been a penalty from even my point of view. It can't always be perfect from the referee's side.
"We just hope we get the right decisions when we feel like we need them."
While many would have expected England to beat Iran, the emphatic scoreline would have impressed even the harshest critics.
Pickford believes the performance was even more impressive given some of the other results, including defeats for Argentina and Germany as well as three goalless draw.
"It was a great game, six goals in the first game - if you look at the previous record of Iran in the last number of games they are hard to beat and hard to break down," added the Everton goalkeeper.
"We were very clinical in our approach. Six goals from 12 shots. The lads were outstanding.
"As a whole squad we want to keep clean sheets because we know how important they are through tournament football.
"You're never going to be happy conceding a goal and we will build on to USA and hopefully get a clean sheet there.
"Iran's record is very good and to manage to score six goals and win the first group game of the World Cup is a big statement as a team and to keep moving forward to the USA game.
"It is what World Cup football is all about. There are going to be surprise, there has been some tight games already, (some) 0-0s.
"There are always going to be surprises in World Cup games, Saudi Arabia played well and got the win."