Their convincing 3-1 victory - sullied by what is feared to be serious knee injury sustained by the Hearts forward - ensured Robbie Neilson's reign as head coach got off to an encouraging start.
But regardless of the level of opposition this season, captain Danny Wilson acknowledges that the expectation levels from the supporters will not fluctuate.
And after last season's relegation following what seemed like an air of resignation over Hearts' fate, the defender knows mediocrity will not be tolerated this time as they aim to bounce straight back into the SPFL Premiership.
Neilson's side face something of a baptism of fire in the Championship, an opening fixture away against Rangers on August 10 followed by the visit of city rivals Hibernian the weekend after.
"With this club there is always expectation and you need to do well," said Wilson. "That's something we need to deal with.
"Last season's challenge was to try and stay in the league. We didn't manage that but now we find ourselves in a league we don't feel the club should be in. I'm sure Hibs and Rangers will say that too. We need to hit the ground running when we go to Ibrox.
"It's a good pressure to have, knowing that anything less than wins would be seen as poor results. You would rather be winning games . We lost far too many last season for my liking. This season I'm looking forward to getting more wins on the board.
"The fans have done great and they have the pressure on us to do well, but we need to be realistic as well.
"We can only be as good as how we start the season. We've got a tough run of fixtures but we'll take it one game at a time, it's the old cliche."
Neilson has overseen a much-needed squad overhaul this summer, welcoming eight arrivals.
One of those recruits, Alim Ozturk, has become Wilson's partner at centre-half.
The Turkish centre-half arrived from Trabzonspor and has shown up well so far.
Wilson says it has not taken them long to form an understanding, especially as Ozturk reminds him of a former Rangers team-mate.
Wilson added: "He has been great, he has settled in really well. He is a good, big player. I've never really played with a centre-half like him, he reminds me a wee bit of Madjid Bougherra - he has that wee bit of arrogance about him. He's good on the ball and is quick and strong."
All of Hearts' goals against Annan came in the first half, with Billy King, debutant Osman Sow and Callum Paterson on target.
Annan substitute Scott Davidson scored a consolation in injury time for the League Two team.
Paterson was taken off on a stretcher on the stroke of half-time after collapsing to the ground clutching his left knee. The right-back is thought to have caught his studs on the pitch.
Paterson is expected to be sent for a scan today, with Neilson admitting the best-case scenario is that he has only damaged his medial ligaments, an injury that could rule him out for two months.
Wilson added: "We've all got our fingers crossed for him because he was a good player for us last season and we really hoped he could kick on this season. We're still hopeful his injury is not too bad and he can be back with us as soon as possible."
Of his side's defeat, Jim Chapman, the Annan Athletic manager, said: "If you defend like that against any player you're going to get punished but the players kept grinding away and we scored what I thought was the best goal of the game."