Ricciardo qualified and finished seventh at Monza, matching his best result of the season, and holding off quicker cars to do so.
He sees the result as continuing the form he has shown in the races following a difficult weekend in the Canadian GP in June.
When asked by AUTOSPORT if it was important to show why Red Bull had picked him in his first race since being announced, Ricciardo replied: "Yeah, definitely. Since Mark's announcement [that he is leaving F1] I have definitely lifted my game.
"Montreal was a disaster for me and we haven't had that disaster since.
"We've started the second half of the season in the points so let's keep going in that direction."
Ten reasons why Red Bull picked Ricciardo
With Sauber scoring heavily thanks to Nico Hulkenberg's fifth place, Ricciardo's points have prevented Toro Rosso's advantage over the Swiss team being cut dramatically in the constructors' championship.
"It was definitely the best we could have done," he said.
"The low downforce paid off for us defending, but for attacking we lost too much time in the second sector.
"I don't think we had the speed to do any better than seventh, particularly with the guys behind coming strong at the end. It was nice to hold them off.
"When we've qualified in Q3 in the last few races we have gone backwards and haven't had the pace, so it's nice to back it up today and get a good points finish."
Ricciardo is due to drive for Red Bull in its Pirelli tyre test later this week.