Ireland flanker Simon Easterby said it had been difficult on an emotional evening for the Scarlets in their final match at Stradey Park.
The Welsh region did beat Bristol 27-0 to go top of EDF Energy Cup Group D but failed to gain a bonus point.
The game brought to an end 129 years at Stradey before the Scarlets move to their brand new 15,000-seater stadium, Parc y Scarlets, next month.
“We had to concentrate on winning the game and building the performance,” said Scarlets skipper Easterby.
“We are frustrated we didn’t get a bonus point but we are pleased that we stopped Bristol scoring.
“It was good to send Stradey Park off with a victory.”
Wales fly-half Stephen Jones added: “It was a great occasion. There were a lot of pre-match nerves.
“We wanted to get a win to give this great stadium a send off. We had to concentrate on the rugby side of things and not let the emotion get to us.”
Scarlets coach Nigel Davies admitted it was difficult to put emotion to one side
“To keep our focus with all the emotion that was going on with the final game has been tough,” said Davies.
“I’ve been involved in some high pressure situations before but nothing ever like this.
“The weight of expectation and the history of the place put a lot of pressure on us.
“Now I am able to sit back and reflect for the first time on the fact we are leaving this place.
“I thought the boys did well and I thought we managed the game better than we have all season. We are disappointed we didn’t get the bonus point.
“But I don’t think that will make a difference because I always felt we would have to go to Northampton and win anyway.“
Bristol coach Richard Hill said it was a strange night for the English club, who are now out of EDF contention with a second defeat.
“It was odd for us because it felt like an exhibition match in many ways,” said Hill who fielded a largely second string side.
“The atmosphere reminded me of the cauldron that Stradey was during the 80s and 90s.
“We had talked in the week about playing a strong side to reflect the occasion, but in the end we decided to play the team we did.”