The Light Blues enjoyed a thrilling Europa League campaign which just fell short in Spain last week when they lost 5-4 in a penalty shoot-out to Eintracht Frankfurt after the final had ended 1-1 after 120 minutes.
Murray, who played a key part in Dave King's boardroom takeover in March 2015 before standing down from his second spell as director in 2018, is still harbouring European disappointment but is looking for Rangers to reassert themselves domestically next season.
He told PA News agency: "As (former Liverpool manager) Bill Shankly said, the league title is your bread and butter.
"That's what you go for at the start of the season and ultimately the league table doesn't lie.
"The best team in the country tends to win the championship. So I think it is really important.
"It is great that both (Old Firm) teams are really strong, there isn't a lot between the teams.
"There is no question that Rangers are back. Celtic did really well last year and you have to praise the new manager (Ange Postecoglou) for the fantastic job."
The summer transfer market is vital in Murray's mind, with new arrivals expected while Connor Goldson and Calvin Bassey are among those linked with moves away.
"Recruitment in football now is absolutely critical and if we get the recruitment right in the summer, we have every chance of winning the league next year," said Murray. "I would be pretty confident.
"I think we should be looking at trading in some players and freshening up the squad.
"Any team needs to be freshened up and whether that is Calvin Bassey or anyone else, every player has a price.
"Bassey has been immense in terms of his end to his season, his whole season.
"It depends on how the manager sees the team and the shape of the team.
"I am a great believer in keeping the spine of the team. There is uncertainty about (veteran goalkeeper) Allan McGregor's future and uncertainty with Connor Goldson's future.
"Having the spine of the team strong and having that foundation is obviously important.
"So yes, a lot of decisions to be made but the good thing is we have assets to look at. It is all pretty positive as far as I am concerned."
Murray first joined the Rangers board in 2007 but was removed in 2011 when Craig Whyte took control of the club, before it descended into administration then re-emerged in the bottom tier of Scottish football in 2012.
He admits he is still feeling sore after the defeat to Frankfurt in what was the Ibrox club's first European final in 14 years, since they lost 2-0 to Zenit St Petersburg in the 2008 Manchester final.
He said: "I have never felt as deflated after a game as I did on Thursday morning.
"I felt really low. It still feels a bit raw even now. It was a tough one to take. It was a great experience but ultimately disappointing.
"I went to Manchester happy to be there, you win it is a bonus. I went last Wednesday fully expecting us to win.
"I was really confident. I thought it was written in the stars and I was just so disappointed.
"We did so well to get there, it was an incredible achievement."