The Scottish champions set up a Betfred Cup quarter-final clash with Alloa in Glasgow after taking Mark McGhee's side apart.
Doubles from Tom Rogic and Moussa Dembele plus a special strike by Scott Sinclair saw the hosts win convincingly in Rodgers' first domestic game at Celtic Park.
The Hoops boss said: "As long as it was a home draw, no matter who it is, w e love to play here and I sense the players are excited about being here
We will respect Alloa like we will any other team."
Rangers were also drawn at home, against Queen of the South, while the only all-Premiership tie sees St Johnstone facing Aberdeen at Pittodrie
After starting the league season with a point against the Dons and following his team's 3-2 comeback win over Hearts in the last 16, Saints boss Tommy Wright is undaunted by the tie
"It's a good draw from us," Wright said
"I'm happy with it
We are in the cup, you have got to beat the best to win it
Aberdeen are one of the best, they have been up there in recent seasons
"So it's a tough draw but not one that we would go into thinking we are massive underdogs."
Aberdeen edged out Ayr United 2-1 at Somerset Park to make the quarter-finals and manager Derek McInnes admitted their early-season programme was hard going
"It's been a tough schedule with three games in six days," he said
"Three long trips too
We got back from Slovenia at four in the morning and had to dust them down for an early kick-off in Perth on Sunday, then had a four-hour journey from Aberdeen to Troon on Tuesday night
"So it has been tough on the players with real physical demands
We've now got our fourth game in nine days at home to Hearts on Saturday.
"But we will gather ourselves and be good to go because it is such an important game."
Morton will host fellow Championship side Dundee United in the other quarter-final with the ties scheduled for September 20-22.
Source : PA
Source: PA