
Second half goals from Ellie Brazil, Abbie Ferguson and Megan Collett before a late consolation saw Saints win 3-1 on Sunday.
It has been a difficult summer for the club, with financial cuts within the Women's side.
Parker noted those restrictions, but insisted he still has a side capable of being competitive this campaign.
"We aren't here to make up the numbers," he said.
"I know we're going to have our challenges and we saw today that it's quite a small squad we've got.
"We had a 17 year old that came on at half-time and other players on the bench were 16 and 18.
"There's going to be times where we have injuries and we're going to have to find another way to win.
"While we've got the players fit, we think we can beat any team, and that's the mindset we have in every game."
Saints host Ipswich Town in their first home match of the new season this Sunday at Eastleigh's Silverlake Stadium (2pm kick-off).