The National League North champions gave a good account of themselves in the early stages before John Askey’s side produced an excellent period in the game – scoring twice through Emmanuel Dieseruvwe and Callum Cooke.
But the Coasters were able to get themselves back into things when Gold Omotayo swept home from John Ustabasi’s pass in first half stoppage time to give Hartlepool something to think about at half-time.
Omotayo saw a half-hearted penalty appeal waved away early in the second half before Pools regained their two goal advantage with Dieseruvwe’s second of the game.
And although he was left frustrated by the defeat, Murray conceded his side were lacking quality in key areas – with Hartlepool showing them where they need to get to if they want to be competitive back in the National League.
"We weren’t good enough, that’s the bottom line,” Murray told TNT Sports.
"We’ve had a realisation, and we’ve seen the gulf, in terms of the levels we need to hit in our first group of games. We’ve faced two of the favourites to go up and we’ve seen the step that we have to make.
"We’re on a whole new learning curve as a team and as a club. Last season we spent nearly every game having 60 or 70 per cent of the ball and dictating games.
"Coming to this level now, teams are faster, they’re stronger, they’re better and the quality is higher and I just felt they were quicker and they were stronger in certain areas and when they needed the quality they brought the quality to the table."
Murray added: “I just thought their better players stood out more than our better players. They showed quality at times and we didn’t stand up to that.
“You have to go through times where things don’t go your way and you get punched on the chin where you learn.
“They’re a good team and I do believe they have more killer edge to them than we have at the minute, but as soon as we give two simple goals away you’re fighting against it then.”