Alan Dickens admitted their was a feeling of frustration among the Saints players despite their bonus-point win against Bristol.
The home side felt they should have made things more comfortable at Franklin's Gardens, rather than needing a Stephen Myler penalty and Harry Mallinder drop goal to earn a 32-26 Aviva Premiership success.
Bristol battled hard, continually pegging Saints back after tries from Louis Picamoles, Mike Haywood, JJ Hanrahan and Tom Wood.
And Dickens said: "There was a feeling of frustration afterwards, but we've got to take the win.
"The frustration was that after we scored our third try, we thought we would be able to go clear, but we lost the ball and they scored.
"Credit to Bristol because they were a much-improved team than the one we faced earlier in the season.
"We knew they would be a team playing with confidence, having won their last four games in all competitions, and fair play to the job Mark Tainton has done with them in recent weeks."
While Bristol's four-match winning streak came to an end, Saints secured their third successive Aviva Premiership victory, moving up to fifth in the league standings.
And Dickens added: "There were some good performances.
"Teimana Harrison carried a lot, Louis Picamoles was excellent and Courtney Lawes stood up and did what we wanted him to do.
"To score four tries was positive, but we're under no illusions that we can get better and we'll have some critical meetings in the week."