Cumbrians' goalkeeper Greg Fleming had pulled off three excellent saves on his league debut to frustrate Orient before he was beaten just before half-time when Scott Cuthbert thundered home a header from a Lloyd James corner.
Two minutes after the break Jamie Ness, on-loan from Stoke, scored with a left-footed volley after another James set-piece.
Goals from Kevin Lisbie after 66 minutes and Tottenham loanee Shaq Coulthirst in added time completed the rout, leaving Kavanagh with much to think about in the week ahead.
"We weren't good enough," Kavanagh said. "I'm disappointed, particularly after the way we played in the first half having contained them for 40 minutes.
"But then we gave away a goal just before half-time, which is the worst time to concede, and then gave away a second straight after. From then, our confidence drained away.
"Leyton Orient are a very good side, they work extremely hard for each other.
"We now have to re-evaluate where we are as a team and get back to the basics and build from there.
"It's amazing that we performed well against a Premier League side last week (Sunderland in the FA Cup) showing intensity and intelligence and then we come up against a team in our own division who are well-organised and full of confidence, but we just couldn't cope.
"We became ragged in the second-half and then confidence becomes a factor in the game.
"Players then start to make the wrong choices and all in all, it was a very poor defeat for us.
"We have to work extremely hard this week, analyse the areas where we had problems and look at how to reach 54 points as quickly as we can."