Gareth Southgate made two changes to the England lineup from their opening Euro 2020 match against Croatia ahead of the clash with Scotland on Friday, bringing in full-backs Reece James and Luke Shaw, while visiting coach Steve Clarke made four changes to his side.
Jordan Pickford was called into action just before the half-hour mark, going down and to his right to parry away a well-struck volley from Scotland's Stephen O'Donnell to keep the score level at 0-0 going into the break.
With England still looking for an opener and Scotland looking dangerous at times, Southgate brought on Aston Villa attacker Jack Grealish just after 60 minutes to try to spark his team's offense to life.
"Fair result, fair play to Scotland they defended well," said Kane after the match. "It wasn't our best performance, but it's another point closer to qualification and that's our ultimate goal. We just have to recover and look forward to next game in a few days.
"[Being substituted] is part of the game, the manager felt that was the right decision so you just have o take it. It is what it is.
"It was a tough game -- Scotland defended really well, made good blocks at the right times when we know no game is going to be easy it's a European Championship and Scotland are playing for their lives.
"We've got another big game in a few days against the Czechs, we want to finish sharp -- it's a point, not what we wanted but it's one step closer to qualifying. One step at a time and we go again."
In the end, Scotland saw out an important result after losing to the Czech Republic in their opening match and both teams were left to settle for a point.
After the match, Southgate said: "I think it was a frustrating night, we know we can play better. Got to give Scotland credit they defended valiantly and played well. We didn't do enough to win the game but after that the thing we have to worry about in tournament football after that is we had to make sure we didn't lose it."
England fans booed the team as they left the pitch and Southgate added: "Our fans are entitled to react however they want - we're disappointed - I understand their reaction, we're expected to beat Scotland, they'll be frustrated by it and in the end we have to deal with that."
The result leaves England still well poised to progress, level on four points with group leaders Czech Republic who they host on Tuesday, while Scotland and Croatia have a point each ahead of their meeting in Glasgow on the same day.