Gordon Strachan has won the title with a rebuilt side

Several newspaper columns have suggested that Kilmarnock's Jim Jefferies' achievements, with lesser resources, are greater.

But Lawwell told BBC Sport: "There's only one person who should get it and that's Gordon Strachan.

"If he doesn't get it, there will be reasons other than football."

Lawwell was speaking after Wednesday's 1-0 defeat of second-top Hearts secured the Scottish title with six games remaining.

And he argues that those outwith Celtic do not realise the size of the job until they start working for the club.

The Celtic job is a massive job Celtic chief executive Peter Lawwell

"It was a tense night against Hearts and we were not at our best, but it was not about that one game, it was about the fantastic turnaround there's been this season," said Lawwell.

"I don't think Gordon has received the credit he deserves from various quarters.

"The Celtic job is a massive job, as is the Rangers job.

"People don't realise how big a job it is until they're working here.

"The fans demand victory every week and there's a great deal of media pressure too.

"Gordon also had to cope with following Martin O'Neill, who was a magnificent manager and a legend.

"He had 10 players up on the board when he arrived as 13 had left.

"And he had to bring new players in while reducing the wage budget.

"In terms of blending those players and adding to them, Gordon has done a great job."

All had not looked well when Celtic failed to qualify for the Champions League group stages, just failing to recover after a 5-0 defeat away to Artmedia Bratislava.

There was also a Scottish Cup exit at the hands of First Division Clyde.

"He went to Bratislava and we had a disastrous start, but I think the game came too early," said Lawwell.