The Parkhead side lost 3-1 in their Europa League play-off second-leg game against Swiss side Sion at Stade de Tourbillon on Thursday night to go out on the same aggregate scoreline.
In his first European foray as permanent boss last season Lennon's side lost to Braga and Utrecht in their respective Champions League and Europa League qualifiers.
The vast majority of Celtic fans, though, backed the Irishman for the remainder of the campaign even though rivals Rangers went on to win the Scottish Premier League for the third time in a row.
That bond will be put under strain after Thursday night's result but asked what he would say to fans who are questioning him, the former Celtic skipper replied: "Just stay with the team.
"No-one is more disappointed than myself.
"If there are some disenchanted supporters, we need to put in good performances on a domestic level and get them back on board as quickly as possible."
After a goalless draw in Glasgow it immediately became an uphill battle when Daniel Majstorovic brought down Guilherme Afonso inside the box with less than a minute on the clock.
After the big stopper had been sent off, Pascal Feindouno, who had a trial at Celtic but was too pricey for the Parkhead club, scored from the spot before adding a second after the break.
Celtic defender Charlie Mulgrew pulled a goal back but any prospects of a comeback were scuppered when Giovanni Sio restored the two-goal lead.
"Even when their second goal went in the players, more than anybody else, felt they were still in the tie," said Lennon.
"We got the goal and we felt we were going to get the result we wanted but we shot ourselves in the foot for the third goal.
"It is disappointing for me and disappointing for the players."