League leaders Birmingham resumed their WSL campaign on Sunday following the mid-season break by beating Nick Cushing’s big-spending Manchester City side 2-0 at Solihull Moors.
And Parker, who guided his side to the Women’s Champions League semi-finals prior to the start of their domestic campaign, insists they fully deserve to be top of the table.
"The gulf between the (perceived bigger) teams and us is purely financial," he told Sky Sports. "We can’t compete on that level but the football pitch is a great leveller.
"They have greater financial resources and with that comes greater contact time and opportunities. If we were full-time it’s a really scary thought what we could achieve.
"The players we have at this football club are fantastic. Their professionalism, application, desire to win and camaraderie is the best we have had at the club. Once you have that anything is possible.
"I’m never surprised with the results we are able to produce. Off the pitch the players and staff strive for every 1%.
"We need that because our contact time is not as high as other clubs in the league, so we have to make every moment count.
"Our performances since the first Champions League game against Arsenal have been really consistent and we have taken points deservedly in the games we have played so far."
Parker admits he has high expectations of his side and he urged his players to build on the momentum they gained in the early part of the season.
"We never settle for anything less than the maximum possible, so being knocked out of the FA Cup (to Arsenal) was bitterly disappointing. We wanted a better end to our FA Cup run this year," he said.
"But in terms of our league form, we have played the big three, the favourites for the title, and took seven points out of nine so we have really laid down a marker so far.
"We mustn't let our standards slip. That has been the message all throughout the break."