Portsmouth have named Richie Barker as their new manager and Steve Coppell as director of football.
Wigan have announced Uwe Rosler as their new manager after agreeing compensation with Brentford.
Villa crashed to a second successive heavy Barclays Premier League defeat on Boxing Day, being thrashed 4-0 at home by Spurs three days after suffering a humiliating 8-0 mauling at Chelsea.
Those two scorelines would suggest major problems for the midlands outfit, not least in defence, while their current league position of 16th - only three points above the relegation zone - also appears worrying.
Prior to the game at Stamford Bridge, though, there had been encouraging signs from Lambert's young team. They had gone six matches unbeaten in all competitions, a sequence which included an impressive 3-1 league victory at Liverpool and a 4-1 win at Norwich in the Capital One Cup quarter-finals.
And as far as Villas-Boas is concerned, Villa must stick with the Scot as manager.
"They were a different team at the beginning," said Villas-Boas - who, like Lambert, was appointed to his present post over the summer.
"When Paul changed the structure to five at the back the results improved for them and they managed to get some important ones.
"I think for them now it is important to find stability defensively, looking at what is happening.
"I think Paul is the right person. He is developing a very young team, and it has nothing to do with teams of the past.
"So hopefully, by him being given time to do that, Villa can achieve the results they want."
As well as Villas-Boas, it seems Lambert has the backing of Villa supporters, who were singing his name even after the goals started going in yesterday.
As for the club's hierarchy, after the game - in which Jermain Defoe put a dominant Spurs side in front in the 57th minute before Gareth Bale added a hat-trick - Lambert stressed he has a "good relationship" with Villa owner Randy Lerner and speaks to him every week.
On the fans, Lambert said: "They are fantastic with the way they have supported us.
"I think they can see what we are trying to do and they were terrific again.
"It was really pleasing to hear them back us, but we know we have to get results."
Lambert was keen to emphasise that the entire Villa team, rather than just the defence, had to take responsibility for the last two results and expressed his confidence that they will be able to bounce back.
He said: "I believe they will do it. There is no pressure on these lads at all.
"They will go again and give us everything - they will.
"Even though people got carried away before about us beating Norwich and Liverpool, I never did and neither did the team.
"We never let them get too high or too low, because the nature of football is that you can get hurt at any moment.
"We had a good chat the other day with them. For a lot of them, this is their first crack at Premier League football.
"It is not just the defence - it is everywhere. It is unfair to criticise the defence.
"We are in this together, and collectively we have to stop this - not just the defenders."
Lambert admitted the amount of game time they are seeing might be catching up with some of his young players, but pointed out that Villa's current injuries were making rotation difficult.
Ron Vlaar (calf), Charles N'Zogbia (knee), Gabriel Agbonlahor (hip) and Andreas Weimann (calf) all missed the Tottenham match and were joined as doubts for Saturday's crunch home clash with 18th-placed Wigan by Nathan Baker, who picked up a hamstring problem during the contest.
Darren Bent (hamstring) and Richard Dunne (groin) have also been sidelined.
The opportunity to strengthen squads is nearing and Lambert insisted the events of the last few days would not affect his thinking for the January transfer window.
Meanwhile, Villas-Boas - whose side are now fourth, level on points with fifth-placed Everton and sixth-placed West Brom - said there was "no truth" in reports linking Tottenham with Inter Milan midfielder Wesley Sneijder.