Livi go into their final five matches in fifth place in the Scottish Premiership, which could be enough for a European place depending on who wins the Scottish Cup.
Fourth spot would definitely seal a European spot and Martindale's side sit five points behind Aberdeen ahead of Saturday's trip to Celtic Park.
"Reaching the top six and a cup final probably has exceeded our expectations," Martindale said.
"For the season to end on a fantastic footing, we need to try and secure European football.
"But if we were to finish sixth and reach a national final, on reflection I think we would all agree that's been a fantastic success for Livingston Football Club.
"I will keep the pressure on and I have a good squad of players who I think will keep the pressure on themselves and keep putting demands on one another.
"The three or four games previously to securing the top six, I think you could see a bit of nervousness in the players in the way they were approaching games and within games we were making mistakes that we hadn't made in the previous 14 games.
"Once we had secured the top six, I think you could see that lifted from the players and they start to play with a bit more freedom.
"There's a fantastic opportunity to finish in fifth and if we can pick up an unexpected three points it would make St Johnstone's job that little bit harder."