Larsson was Britain's top scorer with seven goals as they lost their second qualifying match 47-23 to Italy in Motherwell having been defeated 43-14 by Greece in their opener back in October.
Greece were next up three days later in the three-team tournament with Britain playing in London, at the Crystal Palace National Sports Centre, for the first time since the Olympics last summer.
Larsson again led from the front with ten goals as Britain battled valiantly before going down 32-20 to end their hopes of advancing to the second qualifying phase of Euro 2016.
Britain have one more match of the first phase remaining in Italy in June and Larsson, who played at London 2012, insists improvements were made between the two home games.
"The team performance was better than against Italy on Thursday because we stopped thinking about making mistakes and just played great," said Larsson.
"My own performance was OK but it was a shame that Greece man marked me in the second half and took me out. Maybe I could have helped the other guys more."