A Georgios Samaras header and an own goal by Saints midfielder Chris Millar after the break left Celtic on 78 points after 32 games and needing only a draw against Kilmarnock at Rugby Park next Saturday to be crowned champions.
Mjallby said: "There's six games to go and we want to win it and sure, we want to win it on Saturday but we have a target to improve on last season's points tally."
Headded: "We achieved 92 points and we want to go at least one better so we can say there has been an improvement of the team because that is what you are striving for in management."
Once again Neil Lennon, unhappy about media comments following recent defeats to Kilmarnock and Rangers, was absent from a general press conference with Mjallby saying the manager was "having a break" before outlining his side's target to go one point better than last season, when they finished one point behind Rangers.
"We are delighted," said the former Celtic defender. "We are even closer to clinching the title and it is always great to get back to winning ways, especially after losing two games on the trot.
"Our main target is try to pick 15 points from the last six league games."
Mjallby believes there was unfair criticism of the Parkhead side after losing the Scottish Communities League Cup final to Killie and last week's Old Firm derby at Ibrox, given that Celtic were at one stage 15 points behind Rangers - albeit having played two games less - and having gone on an 26-game unbeaten domestic run.
"I think it has been a wee bit too much," said the Swede.
"We have been on a fantastic run. You have to remember where we were in October and obviously we have turned it around with a great run and now we are only one point from clinching the title."
Source: PA
Source: PA