The Vanarama National League North champions Salford won 2-1 but the Alty boss knows they pushed the fancied Ammies all the way.
Parkinson told us earlier this summer that his side aren’t returning to the division to make up the numbers.
Although he won’t set “silly targets” the manager isn’t running scared of anyone ahead of the big kick off next weekend.
The Robins begin at home to Leamington on Saturday and they are nearly ready according to the Moss Lane manager.
“I thought we played really well against a side you would expect to have a good season,” Parkinson said.
“What we did well was look after the ball and the players have been good in possession - the first half we were excellent at times.
“Salford won this league last year and they beat us with a goal against the run of play. We’ve now got to take this performance into next weekend.”
He added: “We know all about the size of the league and the clubs in it.
“But we think we can have a good year. We’re coming in off the back of history-making season together and although there’s a jump in terms of quality we think we’re up to the challenge.”