Boro kicked off the Northern Premier campaign with a 2-1 loss at Lancaster City on Saturday, and drew 1-1 with Grantham Town at Marston Road on Tuesday.
And Meechan, in joint charge alongside Andy Fearn, said: “We’re still probably in second or third gear.
“We have got a few more gears to go through, but we’re not worried, as we have shown glimpses of what we’re about.”
Evan Garnett got Rangers’ goal up at Lancaster – a consolation after going two down. Jake Charles then scored for Boro against Grantham, before AJ Adelekan equalised for the visitors.
“Saturday was a bit of an anti-climax, really. We didn’t lay a glove on them,” said Meechan.
“It has to be one of the more not-so-great performances of our time here.
“Tuesday night, we played against a very physical team and earned the right to get something out of the game.
“We should have closed the game out, but we defended resolutely for large parts of the game.”
Rangers’ next test is against Matlock Town at home on Saturday.
The club are also readying themselves for a charity auction at the ground on Friday, September 13.
Proceeds from the event, which starts at 7pm with free entry, will go to the Motor Neurone Disease Association after former chairman Jon Downing lost his battle with the illness last November.