Leon Osman believes Everton must come to terms with being considered a "scalp" for the less-fancied teams in the Premier League.
Everton discovered just how defiant Stoke City could be at Goodison Park on Sunday when they had to battle back from 1-0 down to claim a point.
And it was Osman, stand-in captain in the absence of both Phil Neville and Joseph Yobo, who delivered the goods with a fine performance and an excellent 20-yard equaliser.
Robert Huth had earlier headed his first goal for Stoke since his £6m summer move from Middlesbrough, and Everton discovered throughout just how much the Potters wanted to prove themselves against last season's FA Cup finalists and fifth-placed side.
Everton had won five games on the trot in all competitions, but they had to battle hard against Tony Pulis's side, now in their second season in the Premier League and looking more than the long-ball outfit they were branded last term.
Osman said: "Getting back into that top five for a European place is our aim, but it does not get any easier. Clubs like Stoke have spent money and the opposition is getting harder by the week. And we are a target now. We have finished in the top five or so now for the last few seasons so teams fancy their chances and want to do well against us.
"They come to Goodison Park intent on claiming the scalp of a big club now, that is what we have become. They know they have to work hard, but they will step it up and raise their game. That makes it twice as hard for us to break them down.
"It is now all about us finding that next level to be able to cope with such situations, people really want to beat us because of what we have achieved."
Osman claimed his second goal of the season and 31st in his Everton career, but added: "Stoke are always difficult to break down, they were determined not to be beaten and they were very tough opponents.
"We scored one goal, could have had another but it was disappointing we didn't win. I tried a similar shot to the one that I scored with a couple of minutes beforehand and it was a mishit and sailed wide. I was hoping for another opportunity to put that right, and it came very quickly afterwards. This time I did connect properly and it was a very pleasing goal to score. Stoke's tactics were to make the game narrow, and they have so many tall players that just pumping the ball into the box does not seem to worry them."
He added: "We still missed enough opportunities to have won. We were fine with our passing up to their area and then it seemed to break down. And we cannot use the excuse of having been on a long trip to Belarus for a Europa League game earlier in the week. These things are tiring, but we just have to get used to it.
"We want to be playing in such games in midweek and then more big games at the weekend, so if we want to play at that level we must get used to what it entails."
Stoke's manager Tony Pulis believes his side have improved on last season, when they were seen as reliant on Rory Delap's long throws and the high ball into the box. He said: "Our away form was poor last season, but apart from when we went to Liverpool and got battered, we have done better this term.
"We got good away points at Birmingham and Bolton and now we have got another one at a very difficult place like Everton. We have an international break now before we play West Ham at the Britannia stadium. They may be in the bottom three, but I watched them at Manchester City recently and they passed the ball really well. If we turn up expecting a stroll in the park we will be in for a nasty shock."
He added: "We have improved on last season, maybe there was a bit of novelty value about us last season but this time around we are better than we were. We feel that and we have shown that, but if we want to do it consistently it is all about being consistent. There is no point talking about it if we don't back it up with our actions. Everton were so much better than us last season, but this time we seemed a bit more comfortable and were able to cope.
"We are passing the ball, getting our head up. Some people don't think we can do that, but I don't give a damn about that because I know what we are capable of."