Lennon lost out to Queen of the South manager Allan Johnston in his category after being nominated along with Motherwell manager Stuart McCall and Terry Butcher of Inverness, while Hibernian striker Leigh Griffiths beat Celtic midfielder Victor Wanyama to the young player award.
Matthews was named in the SPL team of the year along with Wanyama, Charlie Mulgrew and Kelvin Wilson, but he brushed off the failure to claim any of the main prizes.
The Wales international said: "It's out of our hands who wins what. We know ourselves we have had a brilliant season and the whole team have been amazing.
"It's nice to get four players in the team of the year, but we are not too worried about individual awards. It's a team game."
Matthews, who aims to return from a two-month lay-off with a hamstring injury when Celtic face St Johnstone on Saturday on the day they will receive the SPL trophy, did not take Lennon's failure to heart.
"It's nice to win the award, but he got down to the final four and it's out of our hands if he wins it or not," the former Cardiff player said.
"I think he has been great this season, but so have the other managers."
Meanwhile, SPL clubs made progress in their latest meeting on change when they agreed to seek a merged 42-club structure including top-flight play-offs. SPL chief executive Neil Doncaster bullishly declared the new system could be in place by the start of next season.
On offer to the SFL is a merged league of 42 clubs; an all-through distribution model with more money diverted to the second tier; play-offs involving the 11th-placed team in the top flight and three second-tier clubs; and a pyramid structure ensuring movement into the professional league.
A formal vote is set to be taken later this month. The clubs need to approve the plan by a 22-7 majority, with Rangers excluded from voting as they are still associate members.