The Swiss international striker marked his first starting appearance of the season with a double in the 3-0 Premiership win over Ross County at Celtic Park.
With Japanese forward Kyogo Furuhashi out injured and new signing Giorgos Giakoumakis not yet fully fit, Ajeti is likely to lead the line again for Celtic when they open their Europa League group stage campaign against Real Betis in Seville on Thursday.
“I had nothing to prove because I have been training very well and working very hard every day so I don’t need to prove anything to anyone,” said Ajeti.
“If I play and get starts in games, then I will score. We play with high intensity and high pressing where we create many chances and we will always score lots of goals. It doesn’t matter who scores but if we have the chances, then I’ll be there to score the goals.
“The performance was important for us and we performed as well as we have for the last couple of weeks. We did a lot well today and I’m happy to help the team with goals in what was a tough game.”
Celtic manager Postecoglou, who confirmed that left-back Greg Taylor is a doubt for the Betis match after suffering a recurrence of a shoulder injury, was pleased with his team’s perseverance as they had to wait over an hour before debutant Cameron Carter-Vickers gave them the breakthrough.
“The result was positive, the performance was okay,” said Postecoglou. “We started really well and just needed a goal.
“We lacked a little bit of fluency in the front third. In these games, if you don’t score early it gives encouragement to the opposition and they hung in there and defended well at times.
“We overdid things towards the back end of the first-half but I thought after half-time we got back to being disciplined. We knew at some point we’d be able to break them open and the pleasing thing was that we did that trying to play our football rather than doing different things.”