Celtic won the double in Ronny Deila's first season in charge.
Deila took over from Lennon at the start of the 2014 campaign, and guided the side to the double in his first season at Parkhead.
The Norwegian has got the Bhoys playing with a stylish and attacking brand of football, and Commons is enjoying working under the 40-year-old boss, although he was keen not to overlook Lennon's European achievements.
"Although I feel like we're playing better football and we're in a better place, what we achieved under Neil Lennon was quite remarkable, as far as European football goes," he said.
"We want to try and improve in Europe, but certainly domestically we're doing okay - although there are areas where we want to improve."
Under Lennon, Celtic became regulars in the Champions League, and they claimed some notable scalps during that time, including beating Barcelona.
The Bhoys' success in European competition since Deila has taken over has been more modest, with the side dropping out of the Champions League in the qualification for two seasons running.
Celtic made it to the Round of 32 in the Europa League last term, but they were dumped out by Inter Milan and their task will be to do better this time around.
The Scottish side kicked off their group-stage campaign with a draw against Ajax and face another difficult test against Fenerbahce later this evening.