The Shrimps went down to Nathan Broadhead’s 10th minute goal but, with Fleetwood Town and Gillingham both losing, Adams’ players can look forward to another season in the third tier next year.
Defeat meant they finished the season 19th in League One, two points clear of the drop zone, and maintained the club’s record of never having been relegated.
Fleetwood’s better goal difference ensured they survived and Gillingham joined Doncaster Rovers, AFC Wimbledon and Crewe Alexandra in returning to League Two.
Survival means Morecambe will face Derby County, Peterborough United and Barnsley next season following their relegations from the Championship.
Speaking after Morecambe’s safety was confirmed, Adams said: “Although it wasn’t the result we wanted on the day, other scores in the division went our way and we were able to stay in the division, which is what matters.
“We can celebrate tonight but it’s a bit difficult to celebrate avoiding relegation.
“We were in a difficult position when I came here. We were in the bottom four but we have got through it and it is terrific that we have stayed up for the club and the fans, and we can now look to build on this.
“It has been a really difficult season and a long, hard learning curve for everyone involved with the club.
“I am so pleased we will be playing League One football again next season for everyone involved.”