United exited the competition at the fifth-round stage but remained level with Women's Super League (WSL) opponents Palace for 82 minutes, before conceding a sucker-punch second in added time as the Lasses pushed for an equaliser.
However Joel, who has started the last five games for United, admitted there were more positives than negatives for Newcastle to take from their late defeat in the capital.
"I think we should be proud of ourselves," she said. "We didn't get the result we wanted but I think we competed well, especially in the first half. That's a testament to the hard work we put in during the week because the girls covered every blade of grass.
"It was a really close game at times and we played some good football, so there are a lot of positives to take. We conceded late in the game, and then their second goal was as we pushed for an equaliser and took a big deflection.
"We know we can still be a bit more clinical on the ball and taking care of the final pass, but overall it was a very positive performance, and we've gone toe-to-toe with a WSL side, which will give us confidence moving forward."
With just eight Barclays Women's Championship games remaining, United's focus is on a strong end to the season. Joel believes a spirited display against the Eagles will only boost their chances of achieving that goal.
Becky Langley's side put together an impressive run in this year's Women's FA Cup, coming out victorious against both Middlesbrough Women and Nottingham Forest Women to go one step further than the fourth round they went out in last season.
United's Wales international knows they have set high standards for themselves this season, and she added that she hopes to reach them in the remaining league games.
"It's now all about carrying this momentum with us into the remainder of the season," she said.
"We've got to be confident and know that every game in the league is a chance to pick up three points, and those are the high standards we've set."
Tickets are on sale here for next month's Tyne-Wear derby at St. James' Park against Sunderland Women.
