Goals from Ivan Ramis, Emmerson Boyce and Arouna Kone gave his side a comfortable victory.
Martinez said: "It was a really tense game before it started as both Villa and ourselves are in a similar position. We tried to play in the right way and the result was very important.
"In terms of the performance I thought it was similar to that we showed against Everton and Arsenal in the last two games.
"We were very clinical in both boxes and defended well, keeping (Christian) Benteke quiet. He is a footballer who can make a difference at this level. We covered this threat really well and had very good concentration.
"At the other end I thought we had even more opportunities to score in the closing stages.
"The players applied themselves in a great manner to get the result.
"This season I thought we started very brightly but then had a few difficult moments, particularly in November and December when we have had to cope with a lot of injuries and suspensions.
"This has been tough not to get the rewards on the pitch and its put a lot of pressure on the players.
"Not many foreign players can come into this league and cope with the physical side of the game.
"The know-how is important and the likes of Kone and Ramis are good examples how they have adapted. Being able to play in Germany and Spain has helped them a great deal."