However, after such a powerful show in the scrum and set piece the Worcester chief admitted his team should have avoided any need for a nervous finale.
"We dominated the scrum, dominated the set piece and gave them very few opportunities," said Hill. "We should have won by more points and in the end the last quarter of an hour was quite tough.
"If you look at it in the cold light of day, we were considerably better than Bedford today which is very pleasing. We just weren't clinical enough to put the chances away.
"We should have been points up in the first half and had a spell in the second half when we completely dominated and controlled it with five metre scrums and lineouts. Credit to Bedford for being able to hold out, but we had lots of possession and that is a big boost for us going forward.
"We have come here and won, denied them a bonus point and should have won by more. It was a potential banana skin and we should have won by more - we got held up twice and knocked on at the line - but in the end it became close because they defended well."
Pritchard slotted six kicks for battling Bedford and after the game Hill revealed his frustration at the manner in which his team conceded penalties.
"We are very annoyed about the penalty count," he added. "I will be talking to the referee because we had most of the possession and we were being penalised continually as the attacking side going into contact for holding on.
"The new laws state that when someone tackles they must then realise to allow the tackled player to place the ball. But we were never allowed to do that.
"It was last year's regulations which was a bit of a shame and meant that the good attacking rugby we had was negated because we conceded needless penalties and gave Bedford easy possession. We don't feel that is correct and that hasn't happened this season so I was disappointed.
"But the players showed good discipline and didn't lose their temper, but it certainly made the game more difficult than it should have been."