The legendary sticksman passed away at the age of 67 on January 7 in Santa Monica, California, after a secret three-year battle with a brain tumour.
And Alex has struggled to find the inspiration to pick up his instrument since, only playing for 10 minutes here and there.
Asked if the band has discussed reuniting on stage during an appearance on WFAN's 'Talkin' Golf With Ann Liguori' radio show, the 'Time Stand Still' group's guitarist admitted: ''Not really. It's been difficult.
''After Neil passed in January, I've played very little guitar.
''I don't feel inspired and motivated.
''It was the same thing when [Neil's] daughter died in a car accident in 1997; I didn't really play for about a year.
''And I just don't feel it in my heart right now.
''Every time I pick up a guitar, I just aimlessly kind of mess around with it and put it down after 10 minutes.
''Normally, I would pick up a guitar and I would play for a couple of hours without even being aware that I'm spending that much time. So I know it'll come back.''
Alex, 66, admitted that it's unlikely Rush will be playing any shows in the future, especially given bassist-and-author Geddy Lee, also 66, is preoccupied with other projects.
He continued: ''And I think Geddy working on his book for those couple of years, he was so involved in that book -- which is, by the way, a fabulous book -- when he finished it, he went on a tour for a year promoting it.
''Every time I spoke to him about getting back together, he was, like, 'Yeah, when I get through this, when I get through this.'
''And then always something come up, I guess.
''I don't know if the motivation is there for us to really do anything now. ''We're certainly proud of our track record, and we still love music. But it's different now.''
In a gushing statement after it was announced that Neil had passed away, the band said: ''It is with broken hearts and the deepest sadness that we must share the terrible news that on Tuesday our friend, soul brother and band mate of over 45 years, Neil, has lost his incredibly brave three and a half year battle with brain cancer (Glioblastoma). We ask that friends, fans, and media alike understandably respect the family's need for privacy and peace at this extremely painful and difficult time.
''Those wishing to express condolences can choose a cancer research group or charity of their choice and make a donation in Neil's name.
''Rest in peace brother.''
Neil - who was survived by his wife Carrie and daughter Olivia - joined Rush in 1974 and over the years received numerous awards for his performances - including being inducted into the Modern Drummer Hall of Fame in 1983, making him the youngest ever to be honoured.
He announced he was retiring from the band in 2015 in order to spend more time with his family and, later that year, he played the drums for the group's final show at the Forum in Los Angeles.
However, Geddy insisted shortly afterwards that Neil was ''simply taking a break'' and hadn't quit the band for good.
But in January 2018, Alex confirmed that Rush was retiring due to Neil's health issues, which weren't disclosed at the time.
We help you decide who to give your money to.
Nature-inspired songs we just can't get enough of.
Artists are coming up with different ways to entertain and help out this year.
Put these British films about music at the top of your watch list.
The Mifo O5 PROs are some of the most durable wireless earbuds on the market and we can't recommend them enough.
These songs were written for times like these.
Live musicians take a financial hit during the worst health crisis of a generation.