Spurs saw off Villa only days after their Champions League win over FC Twente.
"It was important because a lot of people say playing in the Champions League means we can't win in the Premier League," Modric told the Spurs website.
"But we showed against good opponents that we can do that and can follow up big matches in the Champions League in the week with good performances on the Saturday."
He added: "They pressed us all over the pitch and it was hard for us to find space but at the end of the half we scored to make it 1-1 and it was a big lift for us.
"We played much better in the second half and showed big character to win. It was a very important win for us."