Chants of 'Sack McLeish' greeted the Scot from some fans on the final whistle of the 1-1 draw with Spurs, despite Villa virtually ensuring top-flight football for another season.
Former Birmingham boss McLeish admits it is has been a difficult season but is adamant he retains the support of club owner Randy Lerner.
He said: "It is as tough a season as I've had. I knew it was going to be a challenge but I've always stood up in the face of adversity.
"I assessed the squad at the start of the season and knew there was a possibility of being in the lower half of the table if we got injuries.
"Randy Lerner has been very supportive. He's sent positive texts in the last few days and there is no indication of an urgent meeting being required."
McLeish can point to a shortage of experience, a lengthy injury list, blooding too many youngsters and having to drastically reduce the wage bill as mitigating circumstances.
But the Scot will still expect better during 2012/13, and he said: "I have taken a lot of weight on my shoulders this season. I was happy to take pressure off the players. I am not going to again next season though. They had better get their finger out."
He continued: "We are assessing next season. It's all been ongoing. We've been assessing it every single week. We've got to start putting a plan of action in place.
"Our early-season form wasn't too bad but, since the New Year, we've had problems to contend with injury-wise.
"To lose two of your most experienced players (Darren Bent and Richard Dunne) for such a long time will hurt any team."