Callum McGregor has urged his Celtic teammates to build on their stunning win over RB Leipzig - and enhance the global reputation of Scottish football by reaching the Champions League knockout rounds.

McGregor helped the Parkhead club to record an unexpected 3-1 triumph over their renowned German rivals in the East End of Glasgow on Tuesday night and move up to 13th place in the table.

The midfielder felt that Brendan Rodgers’ men produced their best performance ever with the ball in Europe’s elite club competition and deserved to defeat the second-placed side in the Bundesliga.

The Celtic captain believes the emphatic victory sets them up nicely for their remaining league phase matches against Club Brugge and Young Boys at home and Dinamo Zagreb and Aston Villa away.

However, he is also wary of getting too carried away with the famous result and has stressed to his fellow squad members they need to try and improve on their display in their final four outings and secure a place in the two-legged play-off in February.

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“Even at half time [in the RB Leipzig match] you think, ‘We’re 2-1 up, let’s finish the job’,” he said. “You don’t want to be a nearly team that plays well and doesn’t get anything from it.

“We’ve set ourselves up really well in the first four games. So now the chance for us is to try and qualify. Can we finish as high up as that table allows us to? We know it’s going to be a big challenge and we have to keep working. But there’s no reason why we can’t.

“That’s where we want the club to be. We’re ambitious people and we want to strive for the best, push this club as much as we can and push the club as far as we can.”

Scotland’s representatives in the Champions League have struggled to compete with the continent’s best during the past two seasons – Rangers had the worst campaign in group stage history two years ago and Celtic have finished bottom of their section in the last two seasons.

Former Scotland internationalist McGregor is pleased the Parkhead club has proved detractors of the game in this country wrong with their showings against Slovan Bratislava, Atalanta and Leipzig this term.

He confessed that he is keen for them to finish in the top 24 and progress to the knockout rounds for the first time since 2012 and only the fourth time in their history.

“It’s great because it’s shining a positive light on the Scottish game as well,” he said. “When we get to this point, more often than not a lot of teams around Europe are looking for the negative story.

“Now it’s hopefully a positive one, especially the last two games. But it’s up to us now to try and finish that job and try and shine Scottish football in the best light possible.”