McLean gave Scotland the start they were aiming for following their opening Euro 2020 qualifying defeat in Kazakhstan when he headed home in the fourth minute in Serravalle.
Alex McLeish’s side started with a verve to their play but it gradually tailed off and there were concerns of an even bigger shock until Johnny Russell netted on the counter-attack in the 74th minute.
Some of the near 3,000 travelling fans booed during and after the game, although they reserved their most vocal criticism for the Scottish Football Association board.
And McLean believes that frustration was only natural.
The Norwich midfielder said: “The fans have got their opinion and we weren’t good enough at times. They are going to have a go at us at times and we need to deal with that.
“I’m sure everybody at some stage this season has had that, it’s something you need to block out and just focus on what you are doing on the pitch.
“At times it wasn’t good enough, we know that, and the fans showed their frustration. We were frustrated as well.
“It was a stuffy San Marino team that we are expected to beat by a comfortable margin and it just wasn’t to be. We had our chances but after the perfect start we just stalled a bit.”
The former St Mirren and Aberdeen player added: “We had them penned in and started playing and for whatever reason we just didn’t seem to click after that, we just didn’t seem to go into the next gear, we didn’t take our chances.
“We were a bit sloppy in the final third and our build-up play and loose in possession and it just filtered through the team.
“And then frustration kicked in. We just didn’t go to that next level that we know we can.”
Scotland were under pressure to get more goals to begin the process of atoning for their defeat in Kazakhstan, especially after Russia won 4-0 at the Astana Arena earlier on Sunday.
“People have spoken about the pressure that’s been put on us, but we are playing for our country, we are privileged and we need to go out and enjoy it and enjoy the pressure that comes with it,” McLean said.