Sinclair scored twice in the Champions League play-off first-leg rout, which all but secured Celtic's place in the group stage.
"I wouldn't say it was easy, I think we made it look easy," said Sinclair, who scored the second and third goals.
"I think every game is so hard and, just the way we played tonight, it probably looked like it was easy."
Own goals by Evgeni Postnikov and Igor Shitov and a James Forrest strike helped towards a comfortable win for Brendan Rodgers' side ahead of Tuesday's second leg in Kazakhstan.
"It was a great night," Sinclair said. "The boys did unbelievable. The scoreboard shows how well we did.
"We got the fifth, but we wanted more and we kept going for the sixth.
"As players, we love these nights. These are the nights you want to play in. The atmosphere's unbelievable.
"We've come such a long way. The team's gelled very well. The gaffer's brought in a couple of new players and I think we'll be ready."
Shitov was credited with Celtic's fifth goal after Leigh Griffiths' shot deflected into the net off the defender.
But Griffiths said: "I'm going to claim it until somebody else tells me otherwise. Until somebody officially confirms it wasn't my goal, I'm going to claim it."
Griffiths set up Sinclair's second goal against the Kazakh side they also beat in the third qualifying round last season and Forrest's low strike and said: "It's a great scoreline for us.
"Last year, we struggled to overcome this tie. It was a last-minute penalty that put us through, but now you see the team's flying. It's a whole different team now. We look forward to Tuesday.
"Anything can happen in football, we've given ourselves a great chance, but the game over there will be a difficult game to play in. We're 90 minutes away from the promised land.
"Hopefully, we go over there and get the job done. Having a clean sheet going over there with a five-goal lead, you would think we're almost there."
The Scotland striker was also pleased at the news international team-mate Stuart Armstrong is close to signing a new Celtic deal.
"We all know what kind of player Stuart is," Griffiths said of the midfielder. "It's a great boost and we want to keep our best players here.
"Stuart seems happy here and we hope the contract gets signed sooner rather than later."
Winger Scott Sinclair says Celtic made a statement with the 5-0 win over Astana.