A 2-0 win over third-place Bristol City on Sunday cut the gap between Saints and the Women’s Super League 2 play-off place to just two points.
With a home game against second-place Birmingham after the upcoming international break, Parker’s charges can gain further ground on their promotion rivals.
Both of Southampton FC‘s goals came in added time against Bristol City, and Parker thinks that shows how they have improved their game management.
There is a belief that Saints can beat anyone in the division, and they were 2-1 winners at Birmingham earlier this season.
“Everyone is willing to fight until the very end. I’m really pleased with that because I think the game management side of things is improving. We are a young squad,” he said.
“You can see that the experience is growing. I’m really pleased for everybody. We have the international break coming up, so some players will go away.
“These three games have been mentally draining, so it will be a good opportunity for some of these players to get a bit of rest.
“The next game is against Birmingham, so they don’t get any easier. That will be a really tough game, and we need to make sure we prepare for that.
“We beat Birmingham away, so we know we can beat them. We can beat anyone. If we can get a positive result, we are right in the hunt for one of those promotion spots.
“We will keep fighting, we will keep doing what we can. We will see what happens. They were outstanding, as they have been in the last three fixtures.
“Against Palace, it was a great performance and a great result. Newcastle was a good performance, but with a couple of moments when we got punished.
“Now, against Bristol City, those are three top sides, and we could have won them all. We’ve got six points. It’s a good return.”
Tegan McGowan has made a strong impression on Parker since joining on loan from Blues in January, while Ellie Hack also impressed when called upon to start at Ashton Gate.
“Tegan has impacted games when she has come on with assists and goals. Today, to come in and get the goal, I’m really happy with that,” Parker added.
“She came in for Michaela McAlonie, who has been outstanding, but then Micky, when she came on, showed what she can do as well.
“With Hack, we thought that Bristol would maybe look to put more balls in behind. I know that she is a very strong defender in those situations.
“I thought that she was fantastic against Jessie Gale. Every time it was put in that channel, she was winning the battle, and that’s why she came in.
“She hasn’t played for a while, so cramp started to happen, which is why she came off. Amy Goddard was great when she came on. This is why it’s a squad game.”