The 32-year-old confirmed that he still has some ways to go before returning to his top fitness and will limit his singles activity as he continues to recover from hip resurfacing surgery in January.
After the match, the three-time grand slam victor admitted that he had needed more time to consider playing singles at the final major of the year, which starts in NY later this month, but was unable to delay his decision to accept a wild card offered by the United States Tennis Association.
Murray said he does plan to enter both men's and mixed doubles at the US Open, the last Grand Slam of the year that starts at Flushing Meadows in a fortnight.
"I think I did OK", Murray is quoted as saying by the ATP Tour's official website. "I think there were a lot of things I would like to have done better but you also have to be somewhat realistic in terms of what you expect". Further, he also added, "I felt like I wanted to be fair for me to maybe try and get a couple of matches in before making a decision like that".
He said: "If I would have taken the wild card and then not played, then I would have been getting loads of questions about my hip and, 'Why has he turned it down?"
"But I'll probably look at just playing doubles and mixed doubles".
"It will be exciting and interesting to see how I get on". Andreescu won in Toronto after Serena Williams retired with back problems.
Next up for Kyrgios is a first career meeting with eighth seed Karen Khachanov in the second round on Wednesday.
In the women's draw, five-time Grand Slam victor Maria Sharapova moved on to a second-round matchup with top-seeded Ashleigh Barty by knocking off fellow wild card Alison Riske 6-3, 7-6 (4). Caroline Wozniacki, the 2018 Australian Open champion, was eliminated by Dayana Yastremska 6-4, 6-4.
British number one Johanna Konta was beaten 3-6, 6-3, 5-7 by Swedish qualifier Rebecca Peterson.
American Sam Querrey and Japan's Yodhihito Nishioka were also winners, Querrey outlasting France's Pierre-Hughues Herbert 7-6 (2) 7-6 (1) and Nishioka defeated Australian Jordan Thompson 7-5 5-7 6-4.
That is to be expected after just two weeks of dedicated practice before his first singles match for seven months.
In other first-round action at Cincinnati, Moldova's Radu Albot upset 14th-seeded Marin Cilic of Croatia 6-4, 7-6 (6).