Nottinghamshire set the hosts 519 to win after three days of dominance at Lords.
But they were thwarted by stiff resistance on the final day by Adam Voges and Nick Compton and had to settle for 10 points and a draw.
The Notts director of cricket said: “It felt a little like the one that got away but we didn’t ever get that close. Nine down is the one that gets away; seven down we could have been there for another hour and a half and not got them.
“But because we played good cricket for four days we do feel a bit deflated about it.
“We bowled with good control, good skills. Jake Ball and Harry Gurney were outstanding at times, Samit Patel bowled nicely so over the course of the four days I’ve got no complaints about the performance. Wins are hard to come by so when you just miss out on one it’s frustrating.”
But Middlesex batter Nick Compton praised his side for their ‘great escape’.
“The great escape. It was a hell of an effort from the guys,” he said. “I don’t think many would have given us a chance when we went in yesterday but the way Gubbo (Nick Gubbings) batted was phenomenal.
“For a young guy who has just come into the team he looked very organised and his guts and determination bode well for everyone.
“Mine wasn’t a good-looking knock by any stretch of the imagination. It felt horrible at times but that’s the beginning of the season and it is difficult. “It’s about finding your feet, finding your confidence and that took a while but in the end I was glad to do a good job for the side and disappointed not to get a hundred on my return to Lords.”