However, Warriors emerged victorious thanks to tries from Miles Benjamin and Penalty Try after a dominant display from the home pack.
"We are relieved to get that one out of the way and really pleased to get the win," said Horstmann. "We feel we didn't play to our potential and there is a lot more to come. But before the game there was a lot of nervous energy and the boys were pretty tense.
"We came out and had a good crack at them, there were opportunities when we could have put try scoring opportunities away, but we are just happy to get the win.
"It's a first game and so there are nerves. We are still developing as a team so the pressure was there. We are pleased to get the win as we have worked hard for it.
"When you study things you look at the basics and how you win ball. As a pack we had to win our lineout and I thought Ed Shervington was outstanding and hit his marker while Craig Gillies called to the right places.
"We executed our plays and come scrum time I thought Matt Mullan and Tevita Taumoepeau dominated. The boys who came off the bench added something so it was a collective effort."
Horstmann also praised a pumped up home support as attention now turns to the away trip to Kingsholm to face local rivals Gloucester Rugby next Saturday.
He added: "It's always been brilliant playing here, but you could sense the crowd were excited as were today to be back in the Aviva Premiership. They showed it and were very vocal.
"There was some good rugby on show and we kept them on their toes. We probably should have given ourselves more breathing space than we did, but a win is a win.
"Now we look forward to a derby and a really tough place to play, especially in front of The Shed. But we are excited and confident, comfortable with how we are playing and we will back ourselves."