Winger Scott Sinclair helped himself to a hat-trick, with further goals from skipper Scott Brown and winger James Forrest in what was a fifth win of the season against Tommy Wright's side.
Celtic have now won seven matches out of seven since the turn of the year, scoring 21 goals and conceding none and Rodgers believes his side are in good shape ahead of thefirst leg of the Europa League tie against the Spanish side.
Hesaid: "It is another good performance, really focused, not giving away too much.
"We know it is a big step up for us on Thursday in terms of quality but I can't complain.
"We are into the middle of February and we haven't conceded a goal, working very hard, players looking fresh and playing at a really good level.
"So it was good preparation. We bring big confidence into the game. We understand the level of opponent.
"We are so excited for the game, it is a great game for us, the first leg of a European tie and we will be ready for it."
It was a record 24th straight victory in domestic cup ties and theNorthern Irishman said: "I didn't want to mention it before, there is enough demand from me on them to perform well and win.
"But the consequence of it is they break a record, another great tribute to how well they have been working for two and half years."
The former Liverpool boss praised Sinclair after the winger took his tally to 16 for the season.
He said: "It is what he does, he is a goal scorer even though he plays off the side.
"The first goal was a great finish and then he is probably one of the few players who could keep up with Olly Burke to get in the box when he squares it.
"The third goal was a wonderful piece of skill and finish."
French midfielder Olivier Ntcham returned from a hamstring injury to take his place on the bench but had to be withdrawn before the game with his place taken by Mikey Johnston.
Rodgers said: "He felt a tightness in his hamstring in the warm-up. It didn't go but he felt it was too much ofrisk. We will probably scan that tomorrow to make sure."
Defender Jozo Simunovic came off at half-time due to illness and Burke hobbled off with an ankle knock but both should be okay for Thursday.
Celtic had beaten St Johnstone2-0 both home and away in the Ladbrokes Premiership before their midweek win over Hibernian and it left the Perth side with five successive defeats.
Saints boss Wright conceded his side were simply "beaten by a far better side."
He said: "Effectively we lost the tie in first nine minutes with two goals.
"They have so much quality. There is no disgrace getting beaten by a team who are at the moment wiping the floor with everybody. We need to accept that and move on."