Jorginho's first-half penalty was enough to get Chelsea's 2022-2023 Premier League campaign off to a winning start on Sunday (AEST), ending a run of four consecutive defeats for the Blues at Goodison Park.
New signings Kalidou Koulibaly and Raheem Sterling started the hard-fought victory, the latter twice coming close to a debut goal, while Marc Cucurella also made his Chelsea bow from the bench.
Having already parted with substantial fees for that trio, Chelsea has also been linked with moves for Leicester City defender Wesley Fofana and Barcelona star Frenkie de Jong.
After Chelsea won its opening Premier League match for the third consecutive season despite failing to produce a fluid performance, Tuchel insisted more recruits are required.
"Yeah, if we can add, we'll add," Tuchel said.
"Maybe not midfielders as a first option but we are open for everything, and I think we can use new energy, new legs, and fresh input to bring us to a new level.
"If not, then we will push this team, but I think we could use some more input and some more quality. We are on it, but we will not tell you."
Having dominated the opening period on Merseyside, winning the second-most corners on record in the first half of a Premier League match (13, second to Tottenham Hotspur's 15 v Aston Villa in December 2012), Chelsea was indebted to Edouard Mendy for making two strong saves to preserve its lead after the break.
Mendy has now kept a clean sheet on 47 per cent of his Premier League starts (31/66) – only Ederson (50 per cent) has a better record among goalkeepers to have started at least 50 games in the competition.
But with Chelsea having struggled for results at Everton in recent seasons, Tuchel was content with the Blues picking up a victory despite not being at its best.
"We struggled last season to get points here, we have the points, a win is a win," he added. "It's most important for everything to get better, because we have to get better.
"I could assume that we are maybe not on our highest level. We have players in, but they came in late, pre-season was a bit turbulent.
"The last week in training was promising, some situations in the first half were quite good, and in the second half we had simply not enough movement on the ball. It was a strange second half without the rhythm from our team and the interruptions, 10 minutes extra time... a bit strange.
"But we hung on and we did what was necessary to keep a clean sheet, so there are positive things and from there we go.
"Very classic that we win 1-0 with a penalty from Jorginho. Like I said, we know that we need to get better but first of all, a win helps us to be open for improvement and for the atmosphere and spirit."
Meanwhile, with Chelsea acquiring Cucurella this week, it looks set to allow fellow wing-back Alonso to leave for Barcelona.
The Spain international was left out of the squad for the trip to Merseyside, and Tuchel confirmed that decision was the result of his desire to join the Blaugrana.
Asked whether Alonso's absence indicated a move to Camp Nou was close, Tuchel said: "That is the case.
"He tries to leave and we agreed to this wish. That's why it would not have made sense to put him on the pitch today.
"He would've been on the pitch otherwise but in this situation, it was the right thing to do."