The Scots were looking for a big win as Rhein Fire had beaten Amsterdam Admirals 24-0 on Saturday, but it proved to be beyond them.
Tony Vinson ran in a touchdown late in the first quarter for the Monarchs and the former Tottenham and England striker Clive Allen kicked the extra point to give them a 7-0 lead.
The Claymores clawed their way back into the game, with their Finnish kicker Kari Gronroos scoring a 30-yard field goal to make it 7-3, but Allen kicked a 23-yard field goal to stretch the lead to seven points again.
However, in the final second of the first half Gronroos scored another field goal to make it 6-10. Then, with four minutes left of the fourth quarter, Gronroos managed a 35-yard field goal to cut it to a single point. But the Finnish kicker failed from 28 yards early in the fourth quarter - a miss which proved all too costly.
In Germany on Saturday, Bobby Phillips scored two touchdowns as Frankfurt Galaxy came back for a 29-17 win over the World Bowl finalists, Barcelona Dragons.
The Dragons led 10-0 in the first quarter on Jesus Angoy's 31-yard field goal followed by Jon Kitma's two-yard pass to Sheddrick Wilson.
Frankfurt then took control of the game, jumping to a 21-10 half-time lead as Phillips burst up the middle for scores of 4 yards and 1 yards, the second coming with 17 seconds left.
Frankfurt announced before the game that they will not be renewing the contract of head coach Ernie Stautner next season, citing differences with team manager Christoph Heyne. Stautner, 72, led the team for three years, leading them to World Bowl appearances in 1995 and 1996.
In Dusseldorf, Derrick Clark rushed for two touchdowns Saturday as Rhein Fire beat Amsterdam Admirals 24-0. Clark, a former Denver Broncos player, scored on short runs of 12 and nine yards in the first half for his seventh touchdown in the past three games.