A double from Gary Hooper and a Joe Ledley strike saw the Hoops come out on top in a 3-0 win against Hibernian at Hampden and add another piece of silverware to their Clydesdale Bank Premier League title.
Lennon's men also impressed on the continental stage this term by reaching the last 16 of the Champions League - including a victory over Barcelona along the way.
The Celtic boss knows his side were expected to deliver the goods domestically, particularly following the plight of Old Firm rivals Rangers.
But he believes a double and a better-than-expected European run means no-one can ask any questions of his players after bringing down the curtain on the campaign in style.
Lennon said: "That's the double and we had a great European campaign.
"For a team that gets nipped at a little bit, they are a great side and I hope they get the respect they deserve.
"People shouldn't be asking questions. Okay, domestically we are expected to do things, but surely no one could have expected what we did in Europe this season.
"People were raising their eyebrows at the qualification stage. Then, when the group stage came out, people were raising their eyebrows at that.
"We overcame it all. They were playing the 59th game of a marathon season. The majority of them will be back in on June 20 so I hope they enjoy their break because they thoroughly deserve it."