The American attacker emerged from the bench in Sunday's match and dabbed a superb assist on Michy Batshuayi's goal to conclude a 4-1 win for the Blues. It was a welcome contribution for Pulisic after he was left out of the matchday squad for last Wednesday's 2-1 Champions League win at Lille.
"Obviously I haven't been getting as many minutes as I would like," Pulisic admitted to reporters, as quoted by Reuters.
"I'm not just going to throw a fit and give up, ever, so if I'm on the bench it doesn't mean the gaffer doesn't think I'm a part of the team.
"Of course (it was tough to be left out at Lille). You want to play, be on the field and be in the team as much as you can and it hurt not to be there but I'm happy I got my opportunity at Southampton."
Pulisic was already crowded out by Mason Mount, Willian, Pedro, and Ross Barkley at Chelsea, and his route into the first team became more obscured when Callum Hudson-Odoi started over the former Borussia Dortmund winger on the south coast. The 21-year-old remains determined to usurp rivals in his position, though, and insists he doesn't feel the weight of the £58-million transfer fee that Chelsea paid for his services.
"This number doesn't mean anything to me," he claimed, as reported by ESPN's Nick Miller. "Obviously, I go out and try to give my best every time I'm on the pitch. I'm not sure what the price tag means to you, but I just have to keep trying to perform at my best for myself and for the team.
"You can't completely ignore (the criticism). I don't live under a rock. I hear things, I see things, but I do my best to block it out. I'm just working hard for myself."