Opposition view: Bath boss frustrated as his side squander chances against Saints
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But the Bath boss was left frustrated with his team’s execution and struggles in the set piece.
Saints bossed the scrum battle and also stood tall against the away side's attempts to drive them back at lineout time.
The hosts found it tough to get out of their own half during the second period and nerves were jangling late on.
But Sam Graham won a crucial breakdown penalty in the final seconds to put the seal on a 24-18 Gallagher Premiership success for the black, green and gold.
"This Premiership is so tight," van Graan said.
"We had an opportunity with the last phase of the game and got turned over one metre from the line.
"Once again, it came down to the last play of the match
"The clear-cut opportunity was the ball we dropped on the right-hand side (when Max Ojomoh was unable to gather a pass).
"Our set-piece execution in the 22 is going to be the big work-on this week."
He added: "It came down to the last play of the game. Potentially one more pick and go then it is a different result.
"We had an opportunity to win the game but we dropped the ball two yards out with a few minutes to go.
"We had enough opportunities but that is why the Premiership is such an incredible competition – the margins between winning and losing are pretty small.
"I would say our set piece in their 22 wasn’t good enough. We had multiple opportunities, a maul that was held up and then some scrum penalties right at the end.
"We definitely had enough opportunities."
Saints got on the right side of referee Adam Leal, winning several scrum penalties on the day.
And van Graan said: "I am frustrated. You get different pictures in different weeks but I will follow it up with the official channels and we have got work to do our side."