Cambridge United head coach Richard Money believed his side deserved their 1-0 victory on their return to the Football League .
Josh Coulson netted the winning goal in the 61st minute after Adam Cunnington had missed an early penalty to secure three points in Cambridge's first League 2 match since 2005.
And their boss says the performance showed that they can compete in Sky Bet League 2 following promotion at the end of last season.
Money commented: "There have been 72 teams all wanting to get their first three points from this first weekend, some are happy and some are not so happy, so we're really pleased to have won the game.
"In the first half it was very even, we've missed a penalty early and had a good chance from a corner but they've carried a threat. We came in at half time 0-0 and it could have been 2-2, then we got stronger and we had the better of the second half. I think 1-0 was about right.
"We asked for an atmosphere that was the same as the second leg against Halifax (in last season's play-offs) and it wasn't much difference. Our support was terrific from the first minute, we were patient, and we've all got our rewards because of it.
"Crucially I think we've set out to prove that we're good enough and over 90 minutes we have been. We've got to prove ourselves over 10, 20, 30 games but on the evidence of the first day it was good. We want to keep improving and I think we can."
Money's opposite number John Sheridan was not disheartened by the performance produced by his team, but was left to rue a failure to take chances that came Plymouth's way.
"I don't think we deserved to lose," he revealed. "I felt quite comfortable during the game. We were coping, I couldn't see us losing and then we do stupid things.
"It lets them have some pressure and gives them some belief. There were three things just before the goal; that probably happened in the minute and a half before they goal and I'm thinking that you're just doing thing that puts us under pressure. I don't know what's going through their minds.
"We've had 11 or 12 corners and five attempts on goal, which isn't too bad. We didn't take chances when we had them and they've taken one they've had. They're organised and strong but I was comfortable during the game, but then we've got scrappy towards the end because we're chasing the game.
"We've got to win as many games as possible as early as possible. I'm not too disappointed with the performance, but we've got to learn quickly and hopefully we will."