Worcester won the first leg of the Championship play-off at the Mennaye Field in Penzance.
The Warriors will take a nine-point cushion in to next week's second leg at Sixways, although even if the Pirates can overcome the deficit they will not be promoted as their ground does not meet the Aviva Premiership entry criteria.
Hill said: "I would have been delighted with a one-point win down here.
"This is only the second time that the Pirates have been beaten here this season and we have done it twice.
"A nine-point margin is a little more comfortable but it is not over by a long way.
"It was a tough old game but it opened up in the second half as the Pirates had to give it a go to get the score back.
"We kicked too much ball to them in the second half and they came back at us. As we know they have a very talented three-quarter line and they caused us a lot of problems in the second half.
"It is normally us that start with a few errors but this time it was the Pirates and that got us into field positions where we took our chances and came away with points to make a good start.
"In the second half the Pirates did step up their game and caused us a few problems in defence and cut our line a few times. There was a bit of hanging on there at times.
"That Cornish Pirates team will not give up - they will battle and battle.
"It was a tough game and both sets of players were suffering cramp at the end on a long day, so it will be a tough affair on our patch."
The Warriors led 18-6 at the interval after tries from wing Miles Benjamin - his 50th for the club - and Andy Goode, with the fly-half also converting his own touchdown and adding two penalties. Rob Cook kicked two penalties for the Pirates.
The home side battled hard after the break but were unable to take advantage of the extra man when Warriors flanker Neil Best was yellow carded just after the hour mark. Cook added two penalties to one from Goode.
Pirates backs coach Harvey Biljon was disappointed with the defeat but he still believes that they are in with a chance of causing an upset next Wednesday in the second leg.
Biljon added: "The ball just didn't bounce our way a couple of times and we didn't get the rub of the green. But I am really impressed by the attitude of the players and they kept playing in that second half.
"If we can go up to Sixways and play at that tempo then I think that we are still in with a opportunity of pushing Worcester right to the edge. We gave away a couple of silly penalties which just began to turn things at times.
"Worcester are a very smart side and I think that they slowed the game down when they were reduced to 14 men. We need to get hold of possession when the opposition are a man down and take advantage of it."
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