The right-back will be sent for a scan tomorrow and head coach Robbie Neilson fears the 19-year-old is facing up to at least eight weeks on the sidelines. The worst-case scenario for the player would be a diagnosis of damage to cruciate ligaments, an injury that could end his season before it starts.
Paterson, who had netted the third goal just moments before catching his studs on the turf on the stroke of half-time, immediately signalled to the bench for assistance before being taking off on a stretcher.
Earlier, Billy King opened the scoring at Tynecastle before debutant Osman Sow found the net. The hosts were denied a clean sheet in injury-time after Annan substitute Scott Davidson found the net with a curling effort from 18 yards.
But Neilson, whose side begin their Championship campaign at Rangers on August 10, was concerned for the welfare of Paterson, who recently signed a new three-year deal.
"He has his leg in a brace and the physio is saying we'll need to get it scanned on Monday," said Neilson, who collected a win in his maiden competitive game in the dugout at the start of the post-administration era.
"We're hoping it's just his medial ligaments (rather than his cruciate). You can't tell with these things until you get them scanned. I think he got a shock and these things are painful, but hopefully it's just his medial and it's a six-to-eight week job, that's the most positive outlook.
"It took the shine off a big day for us, he is a big player for us and he's just signed a new contract."
The injury to Paterson was the low point on what was a relatively straightforward afternoon on the pitch. Neilson named what could be considered his strongest line-up for the visit of the League Two outfit, handing competitive debuts to Neil Alexander, Alim Ozturk, Morgaro Gomis, Prince Bauben and Sow.
King set the tone for a fine personal afternoon with a low drive from outside the area after two minutes that was well held by visiting keeper Alex Mitchell.
The winger then notched the opening goal with a superb individual effort after eight minutes. He exhibited good close ball control inside the box before cutting back from the byline and unleashing a rising effort that skimmed off the head of Annan defender Iain Chisholm on its way to the net.
Hearts enjoyed the lion's share of possession and their dominance yielded a second after 18 minutes when Sow capped his maiden competitive appearance with a goal. The former Crystal Palace forward was forced wide inside the area following a Dale Carrick flick, but Sow calmly slotted a right-footed reverse shot beyond keeper Alex Mitchell.
At this stage, it was all about how many Hearts would score rather than the prospect of Annan forcing themselves back into the tie. Sow had another effort saved before Sam Nicholson rifled a shot over the bar from 15 yards after a neat turn in the box.
Paterson got himself on the scoresheet six minutes before the break when he was afforded space in the box to header King's corner in at the back post. But the half ended on a sour note for Hearts after the player fell to the ground clutching his left knee.
As Paterson received treatment from pyshio Rob Marshall before ultimately being taken off on a stretcher, referee Callum Murray blew for the break. Jordan McGhee was the straight replacement for Paterson at the interval. The hosts should have added a fourth in the 52nd minute but King, after rounding the keeper inside the box from a Sow pass, dragged his effort wide from a tight angle.
A Dale Carrick run and shot was saved by goalkeeper Mitchell and Annan somehow survived the goalmouth scramble that followed. Davidson reduced the Black and Golds' arrears in time added on with a low left-footed shot from 18-yards that curled around the outstretched Alexander.
A phlegmatic Annan Athletic manager Jim Chapman said afterwards: "If you defend like that against any player you're going to get punishment, the players kept grinding away and we scored what I thought was the best goal of the game."