The two-time Premier League and La Liga winner made a remarkable return to the English top flight when Wolves brought the free agent to Molineux.
Lage is hoping to have him available from the bench for the clash with West Ham next week
When asked if Costa has a point to prove on his return to England, Lage said: “I haven’t spoken to him about that, but what is important is what he wants to offer to Wolves.
“When we come with that feeling that we need to prove something, we become more anxious. We don’t want that.
“What this player did at Chelsea and Atletico Madrid was very good, so he brings good energy and good vibes.
“He needs to look forward and not backwards.
“I’ve been asking for a striker with a different profile for the last 15 months, it’s so important for a team to have strikers available to play in the competition.
“One of the good examples is when we played the first half against Tottenham. We did everything so well and found all the spaces inside and outside the box. But there was one space we didn’t find because we don’t have that kind of player, and it was to put the defenders in trouble with crosses.
“We tried to shoot from outside, tried to find dynamics outside the box, but sometimes it’s important to have a tall man. We needed a striker to be aggressive and attack the ball.
“It’s so hard to find strikers. Raul is one of the best in the world, but one is not enough. Tell me one team that doesn’t have two or three good strikers. We played Tottenham, who have Kane, and after they brought on Richarlison. It’s so important to have a player like his profile in the team.”
Wolves moved quick to bring Costa in after new signing Sasa Kalajdzic suffered a serious knee injury on his debut.
Raul Jimenez is also sidelined with a knee injury and Lage hopes Costa can offer similar characteristics to both players.
Lage added: “Diego can be a mix between Raul and Sasa. He’s a guy who can do the run in the channel, play the game between the lines and link-up, and be aggressive when we are pressing – and you can see him in the box to win aerial duels.
“Especially when the teams are compact, we can see him at the first post, between the defenders and at the second post. That’s his threat.
“He knows how to keep the ball, how to link and attack the space. He is that kind of striker with a lot of experience. We want him fit and ready to compete at this level as soon as possible, because he can give us a lot of energy, sometimes in the first XI and sometimes coming from the bench.”